1
A box is pulled at the constant velocity by a horse as shown. For 90.0 [min], the horse provides a constant power rating of 10.8 [W]. If the kinetic friction between the box and the ground is 11.8 [N], what is the speed of the box?
A. 1.37 m/s B. 6.10 x 10-1 m/s
C. 9.15 x 10-1 m/s D. 1.02 x 10-2 m/s
1 Force exerted by horse = kinetic friction = 11.8 N Power = 10.8 W
C. 9.15 x 10 -1 m/s
2
A. B. C. D
An object was displaced by a position-dependent position-dependent force. In universe I, the force is a piece-wise function of position, while in universe II, the force is a linear function of position. Which is the correct relationship between F 1 and F2 so that the net work done in I is equal to t o that of II?
F1 = F2 2F1 = F2 F1 = 2F2 2F = -F
2 Area under the curve. Compare the work done: W1 = W2.
B. 2F1 = F2
3 What is the scalar product of vectors A and B, if = + B
= −
3 = +
B = −
XY – 0 + 0 – XY = 0
4
A block of weight w slides down a rough inclined plane of angle θ. A constant frictional force f k acts on the block so that it moves at a constant velocity v down the incline. What is the total work done on the block as it descends a height h down the incline?
4 A block of weight w slides down a rough inclined plane of angle θ. A constant frictional force f k acts on the block so that it moves at a constant velocity v down the incline. What is the total work done on the block as it descends a height h down the incline?
5
Consider a box of mass 15 kg, that is attached to the spring with k = 550 Nm and initially at rest at point P on a frictionless horizontal surface. It is then pushed by a constant force F.
The speed of the box is 1.5 m/s after the spring is compressed by some distance x. What is the work done by the constant force F if the work done by the spring on the box is -28 J?
A. B. C. D
17 J 28 J 30 J 45 J
5 mass = 15 kg, k = 550 Nm v1 = 0, v2 = 1.5 m/s Wspring-on-box = - ΔUelastic = U1 – U2 = -28 J? K1 + U1 + Wother = K2 + U2 0 + 0 + Wother = ½ mv2 + 28
D. 45 J
7
Consider a heart made of glass compressed by a spring by distance d with spring’s constant of k . If the glass and spring is placed above a horizontal frictionless table of height h, what is the speed of the glass when it reaches elevation of h/3?
7 mgh + ½ kd = ½ mv + mgh/3 2
2
9
Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 120 kg and that of spaceman B is 90. kg. Spaceman A pushes B away from him with B attaining a final speed of 0.50 m/s. What is the final s p e ed o f A ?
A. zero B. 0.38 m/s C. 0.5 m/s D. 0.67 m/s E. 1.0 m/s
9 Following the details of the question 0 = (120 kg)v Af + (90.)vBf 0 = (120 kg)v Af + (90.)(0.50 m/s) final s p e ed o f A =
A. zero B. 0.38 m/s C. 0.50 m/s D. 0.67 m/s E. 1.0 m/s
An 80-kg Batman stands on a window ledge 5.0 m above the floor. Grabbing a rope, he swings down to fight the 70kg villain who is standing directly under the chandelier. He releases the rope just as he reaches the villain. Assume that Batman’s center of mass moves downward 5.0 m. With what speed do the entwined foes start to slide across the floor?
10
10 Batman’s speed just as he reaches the villain: K1 + U1 = K2 + U2 0 + mBgh = ½ mBv2 =
2ℎ
Final speed after the perfectly inelastic collision: mBvi = (mB + mV)vf
5.28 m/s
11 A 2-kg cart, traveling on a horizontal air track with a speed of 3 m/s, collides with a stationary 4-kg cart. The carts stick together. What is the magnitude of the impulse exerted by one cart on the other? A. 0 B. 4 N ·s C. 6 N ·s D. 9 N ·s E. 12 N ·s
11 A 2-kg cart, traveling on a horizontal air track with a speed of 3 m/s, collides with a stationary 4-kg cart. The carts stick together. What is the magnitude of the impulse exerted by one cart on the other?
A. 0 B. 4 N ·s C. 6 N ·s D. 9 N ·s E. 12 N ·s
P of 2-cart system = constant (2 kg)(3 m/s) = (2 kg + 4 kg)v f vf = 1 m/s ΔP ΔP2kg = Pf – Pi – Pi = (2 kg)(1 m/s) – (2 – (2 kg)(3 m/s) = 4 Ns ΔP ΔP4kg = Pf – Pi – Pi = (4 kg)(1 m/s) – 0 – 0 = 4 Ns
12
Three force versus time plots are shown, in Newtons and seconds. Which of the choices is the correct ordering from the smallest to largest impulse?
12 smallest to largest impulse
13
A particle is acted on by a single conservative force with potential energy function as shown. The total mechanical energy is represented by the horizontal dashed line.
Which of the following correctly describes the force at point G?
13
F = -dU/dx
Which of the following correctly describes the force at point G?
15
A particle is acted on by a single conservative force with potential energy function as shown. The total mechanical energy is represented by the horizontal dashed line. If the particle is released from rest at A, which of the following statement/s is/are TRUE?
I. C, E and F are the stable equilibrium points. II. It has the highest kinetic energy at point C and the lowest kinetic energy at point A and G.
conservative forces have potential ener gy 15 Only function and mechanical E = K + U = constant
I. C, E and F are the stable equilibrium points. II. It has the highest kinetic energy at point C and the lowest kinetic energy at point A and G.
17
Consider two blocks m A = 5.00 kg and mB = 3.00 kg respectively, on a horizontal frictionless. Initially, the spring (k = 5.00 x 104 Nm) is neither compressed nor stretched, and block A is at rest. Block B collides elastically to block A with an initial velocity of:
What is the final velocity of block A after the collision?
17
m A = 5.00 kg and m B = 3.00 kg –mBvBi = m Av Af + mBvBf vBf – V Af = –(VBi – V Ai) -12 = 5v Af + 3vBf 4 = vBf – V Af
18
Four 2-kg particles are located at the corners of a rectangle of sides 3 m and 2 m. What is the moment of inertia of this system about the z-axis?
18
Four 2-kg particles are located at the corners of a rectangle of sides 3 m and 2 m. What is the moment of inertia of this system about the z-axis?
I = mr 2 = 2●22 + 2●32 + 2●(22 + 32) = 52 kg m2
19
The position of Popoy, Basha and Trisha is described by the position vector
where t is time. The mass of Popoy, Basha and Trisha is 60.0 kg, 50.0 kg and 40.0 kg, respectively. What is the velocity of the center of mass at any time?
19 Mvcm = mP(dRP/dt) + mB(dRB/dt) + mT(dRT/dt) (150)vcm = (60)( ) + (50)(−) + (40)(2 ) vcm = (140 − 50)/(150)
20
A 16-kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, a distance h from the floor. The moment of inertia of the flywheel is 0.50 kg·m2. When the block is released and the cord unwinds, what is the acceleration of the block?
A. 0.15g B. 0.56g C. 0.84g D. g E. 1.3g
20
Block: m = 16-kg Flywheel: R = 0.20 m, I = 0.50 kg·m2 (1) mg – T = ma (2) TR = (I/R)a mg – (I/R2)
A. 0.15g B. 0.56g C. 0.84g D. g E. 1.3g
= ma
21
A wheel rotates with a constant angular acceleration of π rad/s2. During a certain time interval its angular displacement is π rad. At the end of the interval its angular velocity is 2π rad/s. What is the initial angular velocity?
21
A wheel rotates with a constant angular acceleration of π rad/s2. During a certain time interval its angular displacement is π rad. At the end of the interval its angular velocity is 2π rad/s. What is the initial angular velocity?
π √2 rad/s
25
Pastillas Girl (mG = 80.0 kg) was moving with velocity 3.00 m/s i when she suddenly exploded into two Pabebe Warriors, Pabebe U (m U = 50.0 kg) and Pabebe K (m K = 30.0 kg). If Pabebe U travels 60.0o above the horizontal, while Pabebe K travels 45.0o below the horizontal, what is the speed of Pabebe U?
A. 2.17 m/s B. 2.69 m/s C. 3.51 m/s D. 7.17 m/s
25 Conservation of Momentum: 2 equations, 2 unknowns: Px: (80)(3) = 50 v U cos 60 + 30 v K cos 45 Py:
0 = 50 vU sin 60 - 30 v K sin 45
By elimination method, we arrive at:
A. 2.17 m/s B. 2.69 m/s C. 3.51 m/s D. 7.17 m/s
26 A solid ball and a (solid or hollow) cylinder roll down an inclined plane without slipping. If the ball and the cylinder have equal mass and radius and came from the same altitude of the inclined plane, which reaches the bottom first? I ball = (2/5)MR2; Solid cylinder: I = ½ MR 2; Hollow cylinder: I = MR 2. A. The ball reaches the bottom first. B. The cylinder reaches the bottom first. C. They arrive at the bottom at the same time. D. It depends on whether the cylinder is solid or hollow
26
Mgh = ½ Mvcm2 + ½ (I/R2)vcm2 Mgh = ½ Mvcm2 + ½ cMvcm2 v = sqrt{ (2gh)/(1 + c) } The smaller c, the faster.
A. The ball reaches the bottom first. B. The cylinder reaches the bottom first. C. They arrive at the bottom at the same time. D. It depends on whether the cylinder is solid or hollow
27
Consider an isolated system comprised of two particles A and B. Let F int,i and Fext,i be the individual internal and external forces, respectively, and p A and pB be the momenta of the particles A and B. Which of the following is TRUE about the system of particles?
27Consider an isolated system comprised of two particles A and B. Let F int,i and Fext,i be the individual internal and external forces, respectively, and p A and pB be the momenta of the particles A and B. Which of the following is TRUE about the system of particles?
28 An ant is located on the edge of a Lazy Susan (turntable) with radius R and constant angular speed ω. The ant got dizzy and crawled halfway through the radius of the turntable. By how much did the ant changed its radial acceleration?
A. doubled B. same C. halved D. quartered
28 R2 = R1 /2 ω = constant.
arad = v2/R = ω2R
A. doubled B. same C. halved D. quartered
33 Sarah rides a gigantic spinning disk with an angular speed of 20.0 rev/s. If Sarah is 0.100 m from the center of the disk, what is her linear speed? A. 12.6 m/s B. 6.28 m/s C. 3.15 m/s D. 2.00 m/s
33 ω = 20.0 rev/s 40π rad/s = 126 rad/s v = rω
A. 12.6 m/s B. 6.28 m/s C. 3.15 m/s D. 2.00 m/s
34 A wheel of fortune has an initial angular velocity of
It has a constant angular acceleration so that it can rotate 14.2 revolutions before it stops. Assuming the wheel lies in the x-y plane, what is its angular acceleration?
34 ωf 2 = ωi2 + 2αΔθ Fortunately, we remember to convert rev to rad!
35 A carriage is pulled by a horse at a constant acceleration of 1.0 m/s 2. The radius of the wheels on the carriage is 0.50 m. After 5.0 s, what is its angular displacement if it is initially at rest? A. 50. rad B. 25 rad C. 10. rad D. 5.0 rad
35 atan = Rα Δθ = 0 + ½ αt2
A. 50. rad B. 25 rad C. 10. rad D. 5.0 rad
36 A block with mass m rests on a frictionless, horizontal surface. A cord attached to the block passes over a pulley whose radius is R , to a hanging block with mass 2m. The system begins to accelerate with magnitude a after having been released from rest. What is the magnitude of the net torque on the pulley (I = ½ MR2)?
36
(1) T1 = ma (2) 2mg – T2 = 2ma (3) Στ = (T2 – T1)R Add (1) and (2): 2mg – T2 + T1 = 3ma = (T2 – T1) = 2mg – 3ma
41
A metal rod lies in the xy-plane and it is hinged at the origin. A force
is applied to the rod at
What is the torque in the rod?
41
42 A solid uniform sphere with radius R is spinning about a frictionless axle through its center. Its surface is applied by a frictional force f so that its has an angular acceleration magnitude α0. If the radius of the sphere were reduced half of its size while applying the same f and maintaining its mass, what is its new α2? I = 2/5 MR2
A. 4α0 B. 2α0 C. α0 D. α0 /2
42 Στ = fR = Iα0 (5f)/(2MR0) = α0
A. 4α0 B. 2α0 C. α0 D. α0 /2
43
A solid sphere of mass 25 kg and radius 0.55 m rolls without slipping on a horizontal surface. If its translational kinetic energy as it moves is 50. J, what is its rotational kinetic energy? I = (2/5)MR 2.
A. 10. J B. 20. J C. 30. J D. 40. J
43
M = 25 kg, R = 0.55 m K.E.trans = ½ Mvcm2 = 50. J vcm2 = 2 m/s K.E.rot = ½ (I/R2)vcm2 = (1/5)Mvcm2 since I = (2/5)MR 2.
A. 10. J B. 20. J C. 30. J D. 40. J
44 A solid sphere yo-yo has mass M = 0.25 kg and radius R = 0.5 m. What is the velocity of its center of mass after falling a height h = 5 m from a stationary point? I = ½ MR2.
44
= 8.09 m/s
48
Two objects are attached to ropes that are attached to wheels on a common axle. The two wheels are glued together and have a moment of inertia of 40 kgm 2. The radii are R 1 = 1.2 m and R2 = 0.4 m. If m 1 = 24 kg, what is m 2 such that there is no angular acceleration?