Unit 11: Moments 5. If a nut and bolt are difficult to undo, it may be easier to turn the nut by using a longer spanner. This is because the longer spanner gives A a larger turning moment. C less friction. B a smaller turning moment. D more friction
1. The diagram shows a gauge, which measures the amount of liquid in a tank.
6. A pivoted uniform bar is in equilibrium under the action of the forces shown.
At which position should the pivot be placed so that the pointer moves the greatest distance as the tank is emptied? What is the magnitude of the force F? A2N B4N C8N D 14 N
2. A driver's foot presses on a pedal in a car with a force of 20 N as shown in the diagram.
With what force is the spring pulled? A 2.5 N B 10 N C 100 N D 160 N
7. A uniform beam is pivoted at its midpoint. An object is placed on the beam as shown. Which force will rebalance the system?
A 20 N acting downwards, 40 cm to the right of the midpoint B 20 N acting upwards, 40 cm to the right of the midpoint C 50 N acting downward, 10 cm to the right of the midpoint D 50 N acting upward, 10 cm to the left of the midpoint
E 800 N
3. The diagram shows a uniform beam pivoted at its centre. Forces of 3 N and 4 N act in the directions shown.
8. The uniform beam of weight 30N and length 4m is hinged at end A, as in the next figure. Which is the force F, in N, which must be applied vertically upwards at a distance of 1m from end B so that the beam is horizontal?
What is the size and position of the upward force, which will prevent the beam from turning? size position A 1N X B 1N Y C 7N X D 7N Y
A 60N
B 50N
C 40N
D 30N
E 20N
9. The next figure shows three positions of the pedal on a bicycle, which has a crank 0.20m long. If the cyclist exerts the same vertically downward push of 25 N with his foot, in which case is the turning effect (a) 25 X 0.2 = 5.0 Nm, (b) 0 (c) between 0 and 5 Nm? Explain your answers.
4. A door requires a minimum moment of 32.5 Nm in order to open it.
What is the minimum distance of the handle from the hinges, if the door is to be pulled open with a force at the handle not greater than 50 N? A 0.33 m B 0.65 m C 0.77 m D 1.54 m
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a)
On figure draw arrows to show the other two vertical forces that act on the wheelbarrow. b) Determine: (i) the moment of the 20 N force about the centre of the wheel A, (ii) the distance between points A and M. 14. A metre rule is supported on a knife-edge placed at the 40cm graduation. It is found that the metre rule balances horizontally when a mass which has a weight of 0.45 N is suspended at the 15 cm graduation, as shown in the diagram.
10. A plank of wood is balanced on a brick. A boy stands at a point 30 cm from the centre. Ten 1 kg masses are placed on the plank 1.5 m from the centre on the opposite side and the beam balances. What is the mass of the boy?
11. A light beam is supported at its centre and two forces of 5 newtons and 10 newtons act on it Calculate the moment, about the knife-edge in this balanced condition, of the force due to the mass of the rule, If the weight of the rule is 0.90 N, calculate the position of its centre of gravity.
a) If the beam balances, at what distance from the centre must the 10 newton force act? b) What upward force is exerted by the support on the beam?
15.
12. A light beam is balanced as shown in figure by the force due to the spring acting on one side of the balance point and by a mass of 200 g on the other side. The gravitational force is 10 newtons on every kilogram.
A knife-edge is placed at the 62.0 cm mark of the uniform metre rule shown in the diagram. In order to balance the rule horizontally, a weight of 0.24 N is hung from one end. Show this weight on the diagram and also mark the weight, W, of the rule acting in the correct position. Calculate the weight, W, of the rule.
16.
AC represents a trap door of width 100cm, which is hinged at A. The weight of the trap door is 30 N and its centre of gravity is 45cm from A. An object is placed on the trap door so that its weight of 40 N acts through B, which is 25cm from A. Show on the diagram these two forces and add a force applied vertically at C, which just lifts the door. Calculate the magnitude of this force at C.
a) What is the downward gravitational force acting on the 200g mass? b) What downward force must be exerted by the spring?
13. Next figure shows an empty wheelbarrow, which weighs 80 N. The operator pulls upwards on the handles with a force of 20 N to keep the handles horizontal. The point marked M is the centre of mass of the wheelbarrow.
17. The board shown in the diagram is hinged at A and supported by a vertical rope at B, 3.0 m from A. A boy of
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weight 600 N stands at the end D of the board, which is 5.0 m from the hinge. Neglecting the weight of the board, calculate the tension T in the rope. If the board were uniform and of weight 48 N, calculate the tension in the rope.
This figure shows a plank of mass 5.0 kg and length 3.00 m resting horizontally on two trestles, P and Q, which are a distance of 2.50 m apart. When a student of mass 60.0 kg walks along the plank from one trestle to the other, the plank sags. Calculate the downward force exerted on each trestle when the student is a distance of:
18.
a) 0.50 m from trestle P, (Take g = 10.0 N/kg) b) 1.25 m from trestle P. 21. The diagram shows a building site crane. a) What is the purpose of the concrete block at one end of the jib? b) If the mass of the concrete is 1500kg, what weight force does it have? (Take g = 10 N/kg) Give units with your answer.
A uniform plank, AB, of length 4.0m and weight 500 N is suspended by a vertical rope at each end. A girl of weight 300 N stands in the position shown, 1.2m from the end, A. By taking moments about A, calculate the tension in the rope supporting the end B. Would you expect the tension in the rope at A to be larger or smaller than that in the rope at B? State a reason for your answer.
19. Next figure shows a uniform metre rule, freely pivoted at a point 20 cm from end P.
c) The bucket is being filled with concrete. If the combined weight of the bucket and the concrete is 4500 N, how far out from the centre of the tower should the crane operator position the bucket so that there is no torque about the tower? (Ignore the mass of the jib).Show your working and give units with your answer. The rule is kept horizontal by means of a 120g mass suspended 5.0 cm from end P. a) Write down the size of the vertical force acting 5.0 cm from P.
22. The diagram shows the electromagnet just above an iron rod, which is pivoted at one end. A box is hanging from the other end.
b) Use the principle of moments to help you determine the mass of the metre rule.
20. Ignore the mass of the rod in the following questions. a) What is the mass of the box?
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b) What is the clockwise torque given to the rod by the 3 N force? Include the Sl unit for torque in your answer.
b) Work out the mass of the kumara shown (in kilograms). (Show your reasoning)
c) (i) What principle makes it possible to find the force provided by the electromagnet? (ii) What is the torque provided by the electromagnet? (iii) What is the force provided by the electromagnet? d) Suppose the electromagnet is shifted out until it is 0.6m from the pivot as shown below.
c) The device is not useful for measuring very heavy masses. What is the largest mass Steve could measure with this device? d) Jenny suggests that if they used a slider twice as heavy as the one they are using at present, they could measure much larger masses as well as light ones. Is she right? Discuss. 25. Henry uses the light seesaw shown below to measure Mary's mass.
If the electromagnetic force has the same value as before, what downward force is required on the end to keep the rod balanced? 23. The cyclist finds she has to stand so that her full weight (550 N) is on the pedals. a) In the box provided to the right of the diagram, draw the position of the pedal when she is exerting maximum torque.
a) Use the information in the diagram to calculate Mary's mass. Show your working. b) Could this seesaw method be used to find Mary’s mass on the planet Mars? Explain.
b) Calculate the size of the maximum torque.
24. Steve and Jenni are selling vegetables at an open-air market. Steve sets up a device for measuring the mass of the vegetables. The vegetables are placed in the bucket. Steve slides a slider weight on the rod until it balances the bucket. The mass is worked out from the position of the slider. To help him work this out, Steve records the slider position with some known masses. Here is Steve's data: Steve’s data Mass (kg) 0 0.5 1.0 2.0 3.0
26. The diagram below shows a mousetrap.
Slider position (cm) 4 19 34 64 94
The mousetrap works as follows. As the mouse walks towards the cheese, the plank tips and the mouse falls conveniently near to Boris, the cat. Complete the following calculations to see how far along the plank the mouse can go before the plank tips. a) A customer wants 2.2 kg of tomatoes. Where should Jenny place the slider? (Show your reasoning)
a) Calculate the turning moment of the counter balance weight about the pivot.
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b) The weight of the plank may be taken to act through the 50 cm mark. Calculate the total turning moment of the cheese and the plank about the pivot. c) What is the minimum distance from the support beyond which the mouse will overbalance the trap and make Boris a happy cat?
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Name: Sec 3.
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Class:
Date:
Science (Physics) Worksheet – Moments and Stability 1.
The lamina below has a uniform thickness. Its centre of gravity is likely to be at
In which other position will the card balance on the rule
A.
C. (
2.
A uniform beam is pivoted at its centre, Y, as shown in the diagram below. Two forces of magnitude 3 N and 4 N act upwards at X and Z respectively. If a third force is applied downwards, what is its magnitude and position to prevent the beam from B. turning?
5 A B C D
3.
)
Magnitude 1N 1N 7N 7N
Position X Z X Z
D.
The diagram below shows the cross-sections of 4 so neutral equilibrium?
(
)
Where is the centre of mass of the bus if it does not tilt over when travelling at an angle as shown in the diagram below? 6. Explain how does the design of a racing car increase it
………………………………………………………………
………………………………………………………………
………………………………………………………………. ( )
4.
A triangular piece of card with a triangular hole can be balanced on the thin edge of a ruler, as shown.
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7.
Fig. 7.1 shows a card hanging through a pin P. The card is being pulled to the left. The card has a weight of 2 N and its centre of gravity is at position x. Fig. 7.1 is drawn to scale.
P
x
card is pulled to the right
Fig. 7.1 (a) On Fig. 6.1, (i)
draw the line of action of the weight of the card and label it 'w'.
(ii) draw the perpendicular distance between the pivot and the line of action of the weight and label it 'd'.
[1] [1]
(b) A student cuts the string and the card starts to oscillate. State the position of x when the card stops oscillating. ………………………………………………………………………………...……… …………………………………………………………………………….……......[1] (c) Calculate the moment of the card immediately after the string is cut.
moment = ……………………[2]
50 cm
8.
25 cm
20 cm
30 cm
25 cm 3N
10N W
What is the weight of the uniformed metre rule that is balanced on the pivot?
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1.
1, 2-Dibromoethane, C2H4Br2, reacts with potassium iodide as shown in the equation below.
.................................... ............................... [1]
C2H4Br2 + 3KI → C2H4 + 2KBr + Kl3 A series of experiments was carried out to investigate the kinetics of this reaction. (a)
In a first experiment the concentration of C2H4Br2 was measured during the course of the reaction and a concentrationtime graph was plotted. The reaction was shown to be first order with respect to C2H4Br2. (i)
On the axes below, sketch a graph to show how [C2H4Br2] changed during the course of the reaction.
[C2H4Br2] / mol dm–3
0 0
time /s [2]
(ii)
Show on the graph how you would measure the initial rate of the reaction. [1]
(iii)
How would you use the graph to show that the reaction is first order with respect to C2H4Br2? .............................................
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(iv)
The experiment was repeated using different initial concentrations of C2H4Br2.
...................... [2]
Using the axes below, sketch a graph to show how the initial rate of the reaction changes with different concentrations of C2H4Br2.
initial rate / –3 –1 mol dm s
0
–3
[C2H4Br2] mol dm
0
[1]
(b)
In a second experiment, the initial concentration of KI was varied and the initial rate was measured. The results are shown in the table below.
experiment
[C2H4Br2] /mol dm–3
[KI] /mol dm–3
initial rate /mol dm–3s–1
1
0.50
0.18
0.027
2
0.50
0.72
0.108
Deduce the order of reaction with respect to KI. Show your reasoning. ...................................................... ............................................. ...................... ...................................................... .............................................
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(c)
(i)
Construct the rate equation for the reaction. ............................................. .................................... ............................... [1]
(ii)
Calculate the rate constant, k, for this reaction. State the units for k.
k = ............................ units .................................. [3] [Total 11 marks]
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