244558112-Formal-Homework-Assignment-5.pdf

Formal Homework Assignment 5

10/26/14 10:40 PM

Formal Homework Assignment 5 Due: 11:15am on Tuesday, October 28, 2014 To understand how points are awarded, read the Grading Policy for Policy for this assignment.

Problem 6.5 A construction worker with a weight of 860N stands on a roof that is sloped at 21∘ .

Part A What is the magnitude of the normal force of the roof on the worker? Express your answer to two significant figures and include the appropriate units. ANSWER:

n = 800 N

Correct

Problem 6.30 A 510kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob's rope rope pulls to the left, 15∘ below ∘ horizontal, horiz ontal, with 510 510N of tension. tension. Ellen's Ellen's rope pulls pulls toward toward the the right, right, 26 below horiz horizontal. ontal.

Part A What tension must Ellen maintain in her rope to keep the piano descending at a steady speed? Express your answer to two significant figures and include the appropriate units. ANSWER:

T = 550 N

Correct

Part B What is the tension in the main cable supporting the piano? Express your answer to two significant figures and include the appropriate units. ANSWER:

T = 5400 N

Correct

A message from your instructor... For " A A Friction Experiment", be sure to advance the figures in the lower left hand corner of the problem page to see the choices you have for each part.

A Friction Experiment http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3179130

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⃗ and the magnitude of the acceleration During an experiment, a crate is pulled along a rough horizontal horizontal surface by a force F acceleration along the the x x direction, ⃗ has a component along the measured. The vector F the x x direction direction of magnitude F x . The experiment is repeated several times, with different values of F x each time, while maintaining a constant

a x , is

value for, F y y , the vertical component of F .⃗

Part A Create a plot of the force of static friction, f s , versus versus the x the x component component of the pulling force, F x , for the experiment. Let the point F min min , along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship relationship amongf s , F x , and F min .

Hint 1. Characteristic Characteristics s of static friction There are two important characteristics to keep in mind about the the force of static friction: Only a stationary object can be acted upon by the force of static f riction. f s ≤ µ s n , where µs is the coefficient of static friction and n is the magnitude of the normal force. This inequality means that the actual force of static friction can have any magnitude between zero and a maximum value of µs n .

Hint 2. Find the force of static friction A horizontal force of magnitude F H is exerted on a stationary crate. The maximum force of static friction, f s, max , between the crate and the floor is 15 N. Assume that F H is the only force, besides that of static friction, f s , acting horizontally on the crate. What is f s when no horizontal force is applied to the crate, that is, when F H

= 0 N ? What is f s

when F H

= 10 N ? What is f s

the instant the

crate starts to move? Enter your answers numerically in newtons. Separate each answer with a comma. For For example if the answers are 100, 200, and − 50 N enter 100,200,-50.

Hint 1. Applying 1. Applying Newton's Newton's 2nd law

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3179130

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⃗ and the magnitude of the acceleration During an experiment, a crate is pulled along a rough horizontal horizontal surface by a force F acceleration along the the x x direction, ⃗ has a component along the measured. The vector F the x x direction direction of magnitude F x . The experiment is repeated several times, with different values of F x each time, while maintaining a constant

a x , is

value for, F y y , the vertical component of F .⃗

Part A Create a plot of the force of static friction, f s , versus versus the x the x component component of the pulling force, F x , for the experiment. Let the point F min min , along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship relationship amongf s , F x , and F min .

Hint 1. Characteristic Characteristics s of static friction There are two important characteristics to keep in mind about the the force of static friction: Only a stationary object can be acted upon by the force of static f riction. f s ≤ µ s n , where µs is the coefficient of static friction and n is the magnitude of the normal force. This inequality means that the actual force of static friction can have any magnitude between zero and a maximum value of µs n .

Hint 2. Find the force of static friction A horizontal force of magnitude F H is exerted on a stationary crate. The maximum force of static friction, f s, max , between the crate and the floor is 15 N. Assume that F H is the only force, besides that of static friction, f s , acting horizontally on the crate. What is f s when no horizontal force is applied to the crate, that is, when F H

= 0 N ? What is f s

when F H

= 10 N ? What is f s

the instant the

crate starts to move? Enter your answers numerically in newtons. Separate each answer with a comma. For For example if the answers are 100, 200, and − 50 N enter 100,200,-50.

Hint 1. Applying 1. Applying Newton's Newton's 2nd law


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A horizontal force

is applied to the crate. However, the force of static friction, s , opposes this force and causes the crate to remain stationary, meaning that a x = 0 . From Newton's 2nd law we know that

∑ F x = max . This yields

∑ F x = F H − f s = max = 0 when applied to this specific problem.

ANSWER: 0,10 10,1 ,15 5 f s = 0,

N

ANSWER: A B C D E

Correct Notice that until the pulling force F x exceeds f s, max , the force of static friction is exactly equal in magnitude to the pulling force.

Part B Create a plot of the force of kinetic friction, f k , versus versus the x the x component of the pulling force, F x , for the experiment. Let the point F min , along the horizontal axis, represent the minimum force required to accelerate the crate. Choose the graph that most accurately depicts the relationship relationship amongf k , F x , and F min .

Hint 1. Characteristic Characteristics s of kinetic friction There are three important characteristics to keep in mind about the force of kinetic friction: Only an object that is sliding with respect to a surface can be acted upon by the force of kinetic friction.

⃗ points in a direction that is parallel to the surface of contact and opposes the motion of the object. f k f k = µk n , where µ k is the coefficient of kinetic friction and N is the magnitude of the normal force.


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ANSWER: A B C D

Correct The most important things to keep in mind when dealing with kinetic friction are the following: Only an object that is sliding with respect to a surface can be acted upon by the force of kinetic friction.

⃗ points in a direction that is parallel to the surface of contact and opposes the motion of the object. f k f k = µk n , where µk is the coefficient of kinetic friction and N is the magnitude of the normal force.

Part C After all the trials are completed, a graph of acceleration a x as a function of force F x is plotted. Assuming the presence of both static and kinetic friction, which of the following graphs is most nearly correct?

ANSWER: A B C D

Correct

Problem 6.26

Part A A 5.10kg object initially at rest at the origin is subjected to the time-varying force shown in the figure. What is the object's velocity at

t = 6 s?

Express your answer with the appropriate units.


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ANSWER:

v = 3.92 m s

Correct

Kinetic Friction Ranking Task Below are eight crates of different mass. The crates are attached to massless ropes, as indicated in the picture, where the ropes are marked by letters. Each crate is being pulled to the right at the same constant speed. The coefficient of kinetic friction between each crate and the surface on which it slides is the same for all eight crates.

Part A Rank the ropes on the basis of the force each exerts on the crate immediately to its left. Rank from largest to smallest. To rank items as equivalent, overlap them.

Hint 1. General problem-solving strategy To make reasonable comparisons among forces you should proceed as follows: 1. 2. 3. 4.

Isolate individual objects via free-body diagrams. Identify the forces that act on each object. Determine the acceleration of each object. Finally, apply Newton’s 2nd law to each object.

You may ultimately be able to do this in your head, but if you are not at that stage, you should draw the necessary free-body diagrams to analyze this problem.

Hint 2. Evaluate the effect of friction The coefficient of friction between each crate a nd the surface on which it slides is identical. Ba sed on this fact, is the frictional force a cting on each crate identical? ANSWER:


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yes no

Hint 3. Examine the top chain of crates Examine the entire chain of three masses pulled by rope A, and consider the total frictional force impeding this chain’s motion. To what value of mass is this force proportional? ANSWER:

kg 2 kg 3 kg 4 kg 5 kg 6 kg 1

ANSWER:

Correct

Normal and Frictional Forces Ranking Task Six boxes held at rest against identical walls.

Part A Rank the boxes on the basis of the magnitude of the normal force acting on them. Rank from largest to smallest. To rank items as equivalent, overlap them.

Hint 1. How to approach the problem Since each box is at rest, Newton’s 2nd law states that the forces acting on each box must sum to zero. Apply this fact to the horizontal fo rces acting on each box.


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ANSWER:

Correct

Part B Rank the boxes on the basis of the frictional force acting on them. Rank from largest to smallest. To rank items as equivalent, overlap them.

Hint 1. Determine the direction of the frictional force In which direction does the frictional force on each box act? ANSWER: horizontal only vertical only both horizontal and vertical

Correct

Hint 2. Newton's 2nd law The force of friction on each bo x acts in the vertical direction. Since each box is at rest, Newton’s 2nd law states that the forces acting on each box must sum to zero. Apply this fact to the vertical forces acting on each box.

ANSWER:


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Correct

Problem 5.44 Johnny jumps off a swing, lands sitting down on a grassy 20∘ slope, and slides 3.5 m down the slope before stopping. The coefficient of kinetic friction between grass and the seat of Johnny's pants is 0.5 .

Part A What was his initial speed on the grass? ANSWER: 2.96

m/s

Correct

Problem 6.21 A 4200kg truck is parked on a 16∘ slope.

Part A How big is the friction force on the truck? The coefficient of static friction between the tires and the road is 0.90. Express your answer to two significant figures and include the appropriate units. ANSWER:


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f = 1.1 104 N "

Correct

A message from your instructor... For "PSS 6.2 Dynamics Problems", in the first two parts you will not use any of the numbers a ssociated with the problem. When drawing your free body diagram, be sure to monitor the angles at which you are drawing the forces.

PSS 6.2 Dynamics Problems Learning Goal: To practice Problem-Solving Strategy 6.2 for dynamics problems. A box of mass 3.1kg slides down a rough vertical wall. The gravitational force on the box is 30N . When the box reaches a speed of 2.5m/s , you start pushing on one edge of the box at a 45∘ angle (use degrees in your calculations throughout this problem) with a constant force of magnitudeF p = 23N , as shown in figure. There is now a frictional force between the box and the wall of magnitude 13N . How fast is the box sliding 3.0s after you started pushing on it?

PROBLEM-SOLVING STRATEGY 6.2 Dynamics problems MODEL: Make simplifying assumptions. VISUALIZE: Draw a pictorial representation.

Show important points in the motion with a sketch, establish a coordinate system, define symbols, and identify what the problem is trying you to find. This is the process of translating words into symbols. Use a motion diagram to determine the object’s acceleration vector a ⃗ . Identify all forces acting on the object, and show them on a free-body diagram. It’s OK to go back and forth between these steps as you visualize the situation.

SOLVE: The mathematical representation is based on Newton's second law:

⃗ = ∑ F ⃗ F net i i = m a.⃗

The vector sum of the forces is fo und directly from the free-body diagram. Depending on the problem, either Solve for the acceleration, and then use kinematics to find velocities and positions; or Use kinematics to determine the acceleration, and then solve for unknown forces. ASSESS: Check that your result has the correct units, is reasonable, and answers the question.

Model


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Start by making a simplifying assumption: We will assume all the forces acting on the b ox are constant, so now you can model the box as a particle moving with a constant acceleration.

Visualize

Part A Using our simplified model, in which we know that the forces are constant (but we don't know what their magnitudes are), which of the following motion diagrams would be a reasonable representation of the motion of the box?

Check all that apply. ANSWER: A B C D

Correct Before you start pushing on the box, the box is acted upon by only the gravitational force that pulls the box downward. The resulting acceleration vector is directed downward. It should be noted that there is no frictional force at this point, since the normal force acting on the box from the vertical wall is zero at this point. The important point in the box's motion is the moment when you start pushing on it. At that moment, three possible scenarios may occur. The box may continue to slide down the wall at an increasing speed, but with a smaller acceleration than before because of the opposing effect of the pushing force and frictional force. In this case, a ⃗ would point downward (diagram D). Alternatively, if the opposing effect of the pushing force and frictional force were such that the box's speed would decrease, the box would be slowing down as it moves downward and a ⃗ would point upward (diagram B). Somewhere in between these two cases, a third scenario arises in which the net force on the box is zero and the box slides down the wall at a constant speed (diagram A). Only the direction and magnitude of the net force can tell you which of these scenarios is the correct one for this problem. Keep in mind that in all cases the motion is always vertical, meaning that the horizontal component of the acceleration must be zero.

Part B Still using our simplified model (in which we do not know the magnitudes of the forces), draw a free-body diagram showing all the forces acting on the box after you start pushing on it. The positive y axis is taken to be upward. The black dot represents the box. Since our model is about having constant forces of unknown magnitude, you do not need to draw the vectors to scale, but your final diagram should be physically reasonable. Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The relative lengths of the vectors will not be graded. ANSWER:


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Correct ⃗ If all the vectors in your free-body diagram were drawn with their correct relative lengths, their vector sum F net

⃗ = ∑i F i

would provide some

quantitative information about the box's acceleration. Since this is not the case here, you cannot obtain any further information about the box's acceleration without first performing some calculations based on Newton's second law. Note that in the diagram abo ve, a coordinate system was established so that the positive x axis points to the right and the positive y axis points upward. This is the same coordinate system used throughout the rest of this problem. Keep in mind that you are trying to find the box's speed 3.0s after starting to push on it.

Solve

Part C Find the box's speed vf at 3.0s after you first started pushing on it. Express your answer in meters per second to three significant figures.

Hint 1. How to approach the problem This is a one-dimensional kinematics problem. You are given the box's initial speed and need to calculate its final speed after a certain period of time. You know that motion occurs only in the vertical direction, so there's no need to write down any equation in th e x direction. All you need is a y , the y component of the box's acceleration, which can be calculated by applying Newton's second law in the y direction.

Hint 2. Set up Newton's second law in the y direction Newton's second law states that (F net ) y , the y component of the net force acting on an object, is equal to the y component of the object's acceleration multiplied by its mass, that is, (F net ) y

= m a y .

Using the coordinate system shown in Part B, enter an expression for (F net ) y in terms of the forces acting on the box. Use f , F G , and n for the magnitudes of the friction force, the gravitational force, and the normal force, respectively; use F p for the magnitude of the pushing force. Express your answer in terms of some or all of the variables f , n , F G , and F p .


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Hint 1. Find F py , the y component of the pushing force Enter an expression for the y component of the pushing force, F py . Recall that you push on the box at a 45∘ angle. Use F p for the magnitude of the pushing force. Express your answer in terms of F p , the magnitude of the pushing force. ANSWER:

F py = F p sin(45)

ANSWER:

(F net ) y = ∑i (F i ) y = = f − F G + F p sin(45) = ma y

Hint 3. Determine which kinematic equation to use Which of the following equations is the most appropriate one to calculate the box's speed 3.0s after you first started pushing on it? ANSWER:

v2f y = v2iy + 2a y (y f − y i )

y f = y i + v iy ∆t + 12 a y (∆t) 2 vf y = viy + a y ∆t

ANSWER:

vf = 18.8

m/s

Correct

Assess

Part D Assuming that the angle at which you push on the edge of the box is again 45∘ , with what magnitude of force F p should you push if the box were to slide down the wall at a constant velocity? Note that, in general, the magnitude of the friction force will change if you change the magnitude of the pushing force. Thus, for this part, assume that the magnitude of the friction force is f = 0.566 F p . Express your answer in newtons to three significant figures.

Hint 1. Dynamic equilibrium

⃗ If the box slides down the wall at a constant velocity, its acceleration must be zero. This is the condition for dynamical equilibrium, or F net

= 0⃗ .

Set up again Newton's second law in the y direction as you did in the previous part, keeping in mind that now the magnitude F p of the pushing force is unknown. Use the equilibrium condition (F net ) y

= 0 , and solve for F p .

ANSWER:


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N

F p = 51.8

Correct Your results make sense. If you push with a force of magnitude 23N , as described in Part C, the box will continue to speed up because they component of the net force, and therefore the y component of the box's acceleration, remains negative (i.e., it points downward). In this case, the effect of the pushing force is simply to reduce the magnitude of the box's acceleration. Then, to reduce the box's acceleration further to zero, you need to push with a force of magnitude F p > 23N , as you have just calculated. Note that if you pushed even harder, the acceleration will become positive, causing the box to slow down and possibly come to a stop. These are the three scenarios whose motion diagrams were identified in Part A.

Problem 6.39 A rifle with a barrel length of 61cm fires a 11g bullet with a horizontal speed of 410m/s . The bullet strikes a block of wood and penetrates to a depth of 13 cm .

Part A What resistive force (assumed to be constant) does the wood exert on the bullet? Express your answer to two significant figures and include the appropriate units. ANSWER:

f k = 7100 N

Correct

Part B How long does it take the bullet to come to rest after entering the wood? Express your answer to two significant figures and include the appropriate units. ANSWER:

t = 6.3 10 "

4

#

s

Correct

Problem 6.22 A 1500

kg car skids to a halt on a wet road where µk

= 0.51.

Part A How fast was the car traveling if it leaves 66-m -long skid marks? Express your answer to two significant figures and include the appropriate units. ANSWER:

v = 26 m s


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Correct

A message from your instructor... For Problem 6.49, the angle is m easured with respect to the horizontal. The problem wants the answer to have three significant figures.

Problem 6.49 It's a snowy day and you're pulling a friend along a level road on a sled. You've both been taking physics, so she asks what you think the coefficient of friction between the sled and the snow is. You've been walking at a steady 1.5 m/s , and the rope pulls up on the sled at a 33.0∘ angle. You estimate that the mass of the sled, with your friend on it, is 66.0kg and that you're pulling with a force of 81.0N .

Part A What answer will you give? ANSWER: 0.113

Correct

Problem 6.56 A person with compromised pinch strength in his fingers can exert a force of only 6.2N to either side of a pinch-held object, such as the book shown in the following figure.

Part A What is the heaviest book he can hold vertically before it slips out of his fingers? The coefficient of static friction between his fingers and the book cover is 0.82. Express your answer to two significant figures and include the appropriate units. ANSWER:

w = 10 N


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Correct

A message from your instructor... For Problem 6.42, treat the thrust force just like you would any other force. Even though a careful analysis of thrust can b e complicated, here thrust is used as a generic force, just as if the person was being pulled by a rope. You should also assume he starts from rest.

Problem 6.42 Sam, whose mass is 76kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 210N and a coefficient of kinetic friction on snow of 0.1 . Unfortunately, the skis run out of fuel after only 12s .

Part A What is Sam's top speed? Express your answer to two significant figures and include the appropriate units. ANSWER:

v = 21 m s

Correct

Part B How far has Sam traveled when he finally coasts to a stop? Express your answer to two significant figures and include the appropriate units. ANSWER:

s = 351 m

Correct

A message from your instructor... For Problem 6.55, the coefficient of static friction is 0.5 while the coefficient of kinetic friction is 0.2.

Problem 6.55 A 1.0 kg wood block is pressed against a vertical wood wall by the 12 N force shown.


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Part A If the block is initially at rest, will it move upward, move downward, or stay at rest? ANSWER: upward downward at rest

Correct

Pushing Too Hard A baggage handler at an airport applies a constant horizontal force with magnitude F 1 to push a box, of mass m , across a rough horizontal surface with a very small constant acceleration a .

Part A The baggage handler now pushes a second box, identical to the first, so that it accelerates at a rate of 2a . How does the magnitude of the forceF 2 that the handler applies to this box compare to the magnitude of the force F 1 applied to the first box?

Hint 1. How to approach the problem Apply Newton's 2nd law to the first box to obtain an equation relating the force applied to the acceleration of the box. Then, do the same for the


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second box. Compare these equations to determine the relationship between 2 and 1 .

Hint 2. Identify the forces that act on each box To apply Newton's 2nd law, you must det ermine which forces contribute to the acceleration of each box. Of the following forces, which act along the direction of the box's acceleration? Check all that apply. ANSWER: The normal force exerted by the floor on the box. The weight of the box. The force of static friction. The force of kinetic friction. The force exerted on the box by the baggage handler.

Hint 3. Apply Newton's 2nd law to the first box The first box has mass m and acceleration a . It is pushed with a force of magnitude F 1 . Applying Newton's 2nd law to this box yields which of the following equations?

Hint 1. Newton's 2nd law Newton's 2nd law states that:

∑ F = ma , where ∑ F is the magnitude of the net force on the object, m is the mass of the object, and a is the acceleration of the object along the direction of the applied net force.

Hint 2. Equation for the force of kinetic friction Recall that the force of kinetic friction on a given object moving relative to a surface is f k = µk n , where µk is the coefficient of friction and n is the normal force.

ANSWER:

F 1 + f k = ma F 1 − f k = ma F 1 + ma = −f k f k + ma = −F 1

Hint 4. Apply Newton's 2nd law to the second box The second box has mass m and acceleration 2a . It is pushed with a force of magnitude F 2 . Applying Newton's 2nd law to this box yields which of the following equations? ANSWER:

F 2 F 2 F 2 F 2

− f k = ma − 2f k = 2ma − f k = 2ma − 2f k = ma


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Hint 5. Put it all together In the previous two subparts, you determined that

F 1 − f k = ma and

F 2 − f k = 2ma . Combine these two equations to obtain one equation that contains both F 1 and F 2 . ANSWER:

F 2 = ma + F 1 F 2 = 3ma − F 1 F 2 = 2f k + ma − F 1

ANSWER:

0 ≤ F 2 < 12 F 1 1 F 2 1

≤ F 2 < F 1

F 2 = F 1 F 1 < F 2 ≤ 2F 1 F 2 > 2F 1

Correct Now see if you can apply this problem-solving technique to answer the next question.

Part B Now assume that the baggage handler pushes a third box of mass m/2 so that it accelerates at a rate of 2a . How does the magnitude of the force F 3 that the handler applies to this box compare to the magnitude of the force F 1 applied to the first box?

Hint 1. Apply Newton's 2nd law to the first box The first box has mass m and acceleration a . It is pushed with a force of magnitude F 1 . Applying Newton's 2nd law to this box yields which of the following equations? ANSWER:


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F 1 + f k = ma F 1 − f k = ma F 1 + ma = −f k f k + ma = −F 1

Hint 2. Apply Newton's 2nd law to the third box The second box has mass m/2 and acceleration 2a . It is pushed with a force of magnitude F 3 . Applying Newton's 2nd law to this box yields which of the following equations?

Hint 1. Find the force of kinetic friction Recall that the force of kinetic friction on a given object moving relative to a surface is f k = µk n , where µk is the coefficient of friction and n is the normal force. If f k represents the force of kinetic friction that acts on the first box, what is the force of kinetic friction acting on the third box? ANSWER:

1 f 2 k

f k 2f k

ANSWER:

F 3 − f k = ma F 3 − f k = 2ma

F 3 − 12 f k = 2ma F 3 − 12 f k = ma

Hint 3. Put it all together In the previous two subparts, you determined that

F 1 − f k = ma and

F 3 − 12 f k = ma . Combine these two equations to obtain one equation that contains both F 1 and F 3 . ANSWER:

F 3 = ma − 12 f k F 3 = F 1 − 12 f k F 3 = F 1 + 32 f k + 2ma

Hint 4. Determine the importance of a small acceleration


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You were told in the problem introduction that a is very small. Consider what a very small a implies about the relative sizes of 1 and k . It will help you to consider the following expression:

F 1 − f k = ma . Which of the following statements are correct? ANSWER:

F 1 is much larger than f k . F 1 is slightly larger than f k . f k is larger than F 1 .

ANSWER:

0 ≤ F 3 < 12 F 1 1 F 2 1

≤ F 3 < F 1

F 3 = F 1 F 1 < F 3 ≤ 2F 1 F 3 > 2F 1

Correct

PSS 7.1 Interacting-Objects Problems - Copy Learning Goal: To practice Problem-Solving Strategy 7.1 for interacting-objects problems. A 1260 -kg car pushes a 2160 -kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4510N . Take the friction between the truck's tires and the ground to be 465N . What is the magnitude of the force the car applies to the truck? PROBLEM-SOLVING STRATEGY 7.1 Interacting-objects problems MODEL: Identify which objects are part of the system and which are part of the environment. Make simplifying assumptions. VISUALIZE: Draw a pictorial representation.

Show important points in the motion with a sketch. You may want to give each object a separate coordinate system. Define symbols, and identify what the problem is trying to find. Identify acceleration constraints. Draw an interaction diagram to identify the forces on each object and all action/reaction pairs. Draw a separate free-body diagram for each object. Connect the force vectors of action/reaction pairs with dashed lines. Use subscript labels to distinguish forces that act independently on more than one object. SOLVE: Use Newton's second and third laws. Write the equations of Newton’s second law for each object, using the force information from the free-body diagrams. Equate the magnitudes of action/reaction pairs. Include the acceleration constraints, the friction model, and other quantitative information relevant to the problem. Solve for the acceleration, and then use kinematics to find velocities and positions. ASSESS: Check that your result has the correct units, is reasonable, and answers the question.

Model The car and the truck are separate objects that form the system. Since only the straight-line motion of the car and truck is involved in this problem, model them as particles. The earth and t he road surface are part of the environment. http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=3179130

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Part A Assuming that the car pushes the truck to the right, which of the following free-body diagrams is the correct diagram for the situation described in this problem? In each case, the d iagram on the left refers to the car, and that on the right to the truck. Dashed lines connect action/reaction pairs. The

,⃗ n ⃗ are, respectively, friction, normal force, and gravity; subscripts C and T stand for "acting on car" and "acting on ⃗ , and F following notation is used: f G ⃗ ⃗ truck"; F is the force exerted on the car by the truck. Note that the force vectors are not ConT is the force exerted on the truck by the car; and F TonC drawn in scale.

Hint 1. Draw the free-body diagram for the car Complete the free body diagram of the car by drawing the forces that act on it. Assume the car pushes the truck to the right. Draw the vectors with their tails at the black dot, which represents the car. The orientation of your vectors will be graded. The length of your vectors will not be graded. ANSWER:

Hint 2. Draw the free-body diagram for the truck Complete the free-body diagram of the truck by drawing the forces that act on it. Assume the car pushes the truck to the right. Draw the vectors with their tails at the black dot, which represents the truck. The orientation of your vectors will be graded. The length of your vectors will not be graded. ANSWER:


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ANSWER:


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Correct ⃗ ⃗ ⃗ As the car pushes the truck with a force F . Since F ConT , the truck pushes back on the car with a reaction force F TonC ConT acts on the truck, it ⃗ must be shown on the truck's free-body diagram; similarly, F TonC acts on the car, so it is shown on the car's free-body diagram. There is also a second action/reaction pair that is not shown in the diagram above. When the car pushes against th e ground with a force of 451 0N , the ground pushes back on the car with a force of equal magnitude. To propel forward, the car must be pushing backward against the ground. So,

⃗ , a static friction force acting on the the ground must respond by pushing the car forward. This forward-directed force exerted by the ground is f C car's tires. It is a static friction force because, even though the tires are rolling, the bottom of each tire, where it contacts the road, is instantaneously at rest. Furthermore, note that it is this forward-directed static friction force that propels the system forward! Now that you have identified all the forces acting on the system, don't forget to include the necessary acceleration constraints in your pictorial representation. In this problem, there is only one acceleration constraint: the car and the truck are bo th accelerating along the x direction and at the same rate, so

aC = a T = a x .

A Book on a Table A book weighing 5 N rests on top of a table.

Part A A downward force of magnitude 5 N is exerted on the book by the force of ANSWER: the table gravity

.

inertia

Correct

Part B An upward force of magnitude _____ is exerted on the _____ by the table. ANSWER:


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6 N / table 5 N / table 5 N / book 6 N / book

Correct

Part C Do the downward force in Part A and the upward force in Part B constitute a 3rd law pair?

Hint 1. The force of gravity The force of gravity is another name for the force exerted by the earth (or any astronomical object) on objects near its surface.

Hint 2. Exploring Newton's 3rd law Indicate whether the following statements about Newton's 3rd law are true, false, or indeterminate. 1. 2. 3. 4.

According to Newton's 3rd law, every real force has a unique pair force. The pair force is called a "fictitious force." The force and pair force must act on different point masses. The force and the pair force must always have the same magnitude and must also act in exactly opposite directions.

Enter t for true, f for false, or i for indeterminate for each statement, separating the answers with commas (e.g., if all but the first statement were true, you would enter f,t,t,t). ANSWER:

t, f,t ,t

ANSWER: yes no

Correct

Part D The reaction to the force in Part A is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____ .

Hint 1. The force of gravity The force of gravity is another name for the force exerted by the earth (or any astronomical object) on objects near its surface.

ANSWER:


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5 N / earth / book / upward 5 N / book / table / upward 5 N / book / earth / upward 5 N / earth / book / downward

Correct

Part E The reaction to the force in Part B is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____. ANSWER: 5 N / table / book / upward 5 N / table / earth / upward 5 N / book / table / upward 5 N / table / book / downward 5 N / earth / book / downward

Correct

Part F Which of Newton's laws could we have used to predict that the forces in Parts A and B are equal and o pposite? Check all that apply. ANSWER: Newton's 1st law Newton's 2nd law Newton's 3rd law

Correct Since the book is at rest, either Newton's 1st or 2nd law can tell us that the net force on it must be zero. This means that th e force exerted on it by the earth must be equal and opposite to the force exerted on it by the table.

Part G Which of Newton's laws could we have used to predict that the forces in Parts B and E are equal and o pposite? Check all that apply. ANSWER: Newton's 1st law Newton's 2nd law Newton's 3rd law

Correct


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Problem 7.1 A weightlifter stands up at constant speed from a squatting position while holding a heavy barbell across his shoulders.

Part A Draw a free-body diagram for the barbells. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER:

Correct

Part B Draw a free-body diagram for the weight lifter. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER:


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Correct

Blocks in an Elevator Ranking Task Three blocks are stacked on top of each other inside an elevator as shown in the figure. Answer the following questions with reference to the eight forces defined as follows. the force of the 3 kg block on the 2 kg block, F 3 on 2 , the force of the 2 kg block on the 3 kg block, F 2 on 3 , the force of the 3 kg block on the 1 kg block, F 3 on 1 , the force of the 1 kg block on the 3 kg block, F 1 on 3 , the force of the 2 kg block on the 1 kg block, F 2 on 1 , the force of the 1 kg block on the 2 kg block, F 1 on 2 , the force of the 1 kg block on the floor, F 1 on floor , and the force of the floor on the 1 kg block, F floor on 1 .

Part A Assume the elevator is at rest. Rank the magnitude of the forces. Rank from largest to smallest. To rank items as equivalent, overlap them.

Hint 1. Newton's 3rd law Newton’s 3rd law states that when two objects exert forces on each other, these forces are always equal in magnitude and opposite in direction.

Hint 2. Contact forces If two objects touch each other, they exert forces on each other according t o Newton's 3rd law. If two objects do not touch each other, they cannot exert forces on each other. (Here we are assuming that the forces of gravity and electromagnetism between the objects are n egligible.)


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For instance, the blocks with masses 1

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g and 3 g are not in contact, therefore, the force

1 on 3 must be zero. While statements such as

"block 3 applies a force to block 1 that is transferred through block 2" might sound reasonable, in physics such statements don't make sense.

ANSWER:

Correct

Part B Now, assume the elevator is moving upward at increasing speed. Rank the magnitude of th e forces. Rank from largest to smallest. To rank items as equivalent, overlap them.

Hint 1. Effects of acceleration If the elevator is accelerating, the net force on each block cannot be zero. However, note that the forces you are asked to compare do not comprise the net force on any of the blocks.

ANSWER:


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Correct

Problem 7.5 Block A in the figure is heavier than block B and is sliding down the incline. All surfaces have friction. The rope is massless, and the massless pulley turns on frictionless bearings. The rope and the pulley are among the interacting objects, but you'll have to decide if they're part of the system.

Part A Draw a free-body diagram for the block A. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER:


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Correct

Part B Draw a free-body diagram for the block B. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER:

Correct Score Summary:


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244558112-Formal-Homework-Assignment-5.pdf

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