4.1 Mechanics and Materials - Moments 2 – Questions Q1. (a) State the principle of moments. ______________________________________________________________ _____ ______________________________________________________________ _____ ______________________________________________________________ _____ (2) (b) The diagram shows a uniform metre ruler, AB, freely pivoted at its centre of mass. Explain what is meant by the centre of mass. ______________________________________________________________ _____ ______________________________________________________________ _____ (1) (c) A 1.0 N weight is placed on the ruler 0.30 m from the middle of the ruler towards A. (i) Explain which way the pivot must be moved in order for equilibrium to be restored. _________________________________________________________ _____ _________________________________________________________ _____ _________________________________________________________ _____ _________________________________________________________ _____ Page 1 of 32
Transcript
4.1 Mechanics and Materials - Moments 2 – Questions
(c) The system is displaced so that the lower bar is no longer horizontal. Explain briefly whether this has any effect on the equilibrium of the system
(b) The system shown in the diagram below is in equilibrium. The uniform rod, CD, has a weight of 15 N and is suspended by two lengths of string, A and B. A ball of weight 3.0 N is attached to the rod in the position shown.
(i) Accurately draw an arrow onto the diagram to represent the weight of the rod. You need not represent the magnitude of the weight.
(2)
(ii) X is the point at which string A is attached to the rod. By taking moments about point X, determine the tension in string B.
(b) To increase the extension of a stiff spring for a given load, a student set up the system shown in the diagram. The weight of the metal bar was 5.0 N and the tension the student achieved in the spring was 37 N.
the gravitational field strength, g = 9.8 N kg–1
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(i) Apply the principle of moments to calculate the mass of the load that the student used.
(4)
(ii) Calculate the magnitude of the force exerted on the metal bar at the pivot.(1)
(iii) Draw on an arrow on the diagram to show the direction of the force calculated in part (ii).
(1)
(c) The spring stiffness k of the spring was 550 N m–1. Calculate the energy stored in the spring.
(2)(Total 11 marks)
Q5.(a) Define the moment of a force about a point.
(2)
(b) The diagram below shows a model bridge consisting of a uniform plank of wood. The plank is 1.0 m long and weighs 10 N. A toy car of weight 5 N is placed on it. The bridge is suspended from a rigid support by two strings and is in equilibrium. The plank does not touch the shaded blocks.
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(i) Show and label the forces acting on the bridge.(2)
(ii) By taking moments about point P, calculate the tension in string A.(3)
(b) The diagram below shows a horizontal beam pivoted close to one end. The beam is supported by a spring and is loaded with weights of 2.0 N and 5.0 N as shown. All dimensions are marked on the diagram and are measured from the pivot.
By taking moments about the pivot, calculate the tension in the spring when the beam is horizontal.
Tension = ____________________(3)
(Total 6 marks)
Q8.The diagram below shows a student standing on a plank that pivots on a log. The student intends to cross the stream.
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(a) The plank has a mass of 25 kg and is 3.0 m long with a uniform cross-section. The log pivot is 0.50 m from the end of the plank. The student has a mass of 65 kg and stands at the end of the plank. A load is placed on the far end in order to balance the plank horizontally.
Draw on the diagram the forces that act on the plank.(3)
(b) By taking moments about the log pivot, calculate the load, in N, needed on the right-hand end of the plank in order to balance the plank horizontally.
Gravitational field strength, g = 9.8 N kg–1
Load ____________________(3)
(c) Explain why the load will eventually touch the ground as the student walks towards the log.
Q9.The diagram below shows three children A, B and C sitting on a balanced, horizontal see-saw of mass 35 kg. The centre of mass of the see-saw is vertically above the pivot.
A has a weight of 650 N and B has a weight of 550 N. A sits 1.2 m from the pivot and B sits 0.5 m from the pivot of the see-saw.
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(a) C sits 2.1 m from the pivot.
By taking moments about a suitable point, calculate the weight of C.
Weight of C ____________________(3)
(b) Calculate the force on the pivot of the see-saw.
gravitational field strength of Earth, g = 9.8 N kg−1
Force on pivot ____________________(2)
(Total 5 marks)
Q10.(a) State the principle of conservation of momentum.
(b) Two carts A and B, with a compressed spring between them, are pushed together and held at rest, as shown in Figure 1. The spring is not attached to either cart. The carts are then released. Figure 2 shows how the force, F, exerted by the spring on the carts varies with time, t, after release.
Figure 1
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Figure 2
When the spring returns to its unstretched length and drops away, cart A is moving at 0.60 m s–1.
(i) Calculate the impulse given to each cart by the spring as it expands.
(2)
(ii) Calculate the mass of cart A.
(2)
(iii) State the final total momentum of the system at the instant the spring drops away.
(1)
(Total 7 marks)
Q11.The diagram below shows a laboratory experiment to test the loading of a uniform horizontal beam of weight W. The length of the beam is 1.50 m. The load, M, has a weight of 100 N and its centre of mass is 0.40 m from the pivot. The beam is held in a horizontal position by the tension, T, in the stretched spring.
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(a) Add clearly labelled arrows to the diagram above so that it shows all of the forces acting on the beam.
(2)
(b) The tension, T = 36 N. Calculate the moment of T about the pivot.
Moment ____________________(2)
(c) Calculate the weight, W, of the beam.
Weight W ____________________(3)
(Total 7 marks)
Q12.A student set up the apparatus shown in the figure below to demonstrate the principle of moments.
(a) Using the values on the figure calculate:
(i) the magnitude of the moment about the pivot due to the tension of the spring in the spring balance;
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moment due to spring tension ____________________(1)
(ii) the magnitude of the moment about the pivot produced by the 2.0 N weight;
moment due to 2.0 N weight ____________________(1)
(iii) the weight of the wooden bar.
weight ____________________(1)
(b) (i) Calculate the magnitude of the force exerted on the bar by the pivot.
magnitude of force ____________________(1)
(ii) State the direction of the force on the pivot.
The mass of a retort stand and clamp is 1.6 kg and their combined centre of mass lies along the line XY. A spring which has a negligible mass is attached to the clamp and supports a mass of 0.90 kg, as shown in the diagram. The spring requires a force of 6.0 N to stretch it 100 mm.
(c) If the mass is lifted up and released, it will vibrate about the equilibrium position. Explain, without calculation, why the stand will tip if the amplitude exceeds a certain value.
(b) (i) A uniform plank of length 1.5 m and mass 9.0 kg is placed horizontally on two narrow vertical supports as shown. A block, X, of mass 3.0 kg is placed at the end of the plank immediately above the centre of the right-hand support.
Calculate the magnitude of the downward force on
the right-hand support, ___________________________________________
Q15.A public house sign is fixed to a vertical wall as shown in the diagram.
A uniform metal bar 0.75 m long is fixed to the wall by a hinged joint that allows free movement in the vertical plane only. The wire is fixed to the wall directly above the hinge and to the free end of the horizontal metal bar. The wire makes an angle of 40° with the wall.A single support holds the sign and is mounted at the mid point of the metal bar so that the weight of the sign acts through that point.
(a) (i) Draw on the diagram three arrows showing the forces acting on the metal bar, given that the system is in equilibrium. Label the arrows A, B and C.
(ii) State the origin of the forces.
A ____________________________________________________________
B ____________________________________________________________
C ____________________________________________________________(5)
(b) The combined mass of the metal bar and sign is 12 kg and the mass of the wire is negligible. By taking moments about the hinged end of the bar, or otherwise, calculate the tension in the wire.
(b) The diagram shows a uniform diving board of weight, W, that is fixed at A. The diving board is supported by a cylinder at C, that exerts an upward force, P, on the board.
(i) By considering moments about A, explain why the force P must be greater than the weight of the board, W.
Q17.The diagram shows a uniform bar, AB, which is 1.6 m long and freely pivoted to a wall at B. The bar is maintained horizontal and in equilibrium by an angled string which passes over a pulley and which carries a mass of 2.0 kg at its free end.
(a) The pulley is positioned as shown in the diagram, with the string at 30° to the vertical.
(b) A mass, M, is attached to the bar at a point 0.40 m from A. The pulley is moved horizontally to change the angle made by the string to the vertical, and to maintain the rod horizontal and in equilibrium.Determine the largest value of the mass, M, for which this equilibrium can be maintained.
(b) The see-saw shown in the diagram consists of a uniform beam freely pivoted at the centre of the beam. Two children sit opposite each other so that the see-saw is in equilibrium.
(ii) State the unit of moment ____________________(3)
(b) The long arm of the car-park barrier shown in the diagram is a tube of mass 12.0 kg which is free to rotate about a fixed pivot P near one end. A counterweight is attached firmly to one end of the tube so that the barrier is in equilibrium with its long arm horizontal. Points C and T on the diagram show the locations of the centre of mass of the counterweight and tube, respectively.
(i) Draw on the diagram the lines of action and directions of all the forces acting on the tube and counterweight.
(b) The waiter places a glass on the tray. State and explain where the glass should be positioned on the tray if the force, P, is to have the same value as in part (a).
Q21.A uniform wooden beam of mass 35.0 kg and length 5.52 m is supported by two identical vertical steel cables A and B attached at either end, as shown in Figure 1.
Q22.The diagram shows a uniform door hanging from two hinges 2.5 m apart.
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The moment of the couple that the hinges exert on the door is
A 150 N m
B 200 N m
C 250 N m
D 500 N m(Total 1 mark)
Q23.The rectangular objects, A, B, C and D are each 2 cm long and 1 cm high. Which one of the bodies is in equilibrium?
(Total 1 mark)
Q24.A uniform square block is sliding with uniform speed along a rough surface as shown in the diagram.
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The force used to move the block is 200 N. The moment of the frictional force acting on the block about the centre of gravity of the block is
A 150 N m, clockwise
B 150 N m, anticlockwise
C 300 N m, clockwise
D 300 N m, anticlockwise
(Total 1 mark)
Q25.In the system shown a light rigid beam, pivoted at X, is held in position by a string which is fixed at Y. The beam carries a load of 200 N. The load is moved towards X. Which one of the following statements is correct?
A The tension in the string increases
B The compression force in the beam increases
C The moment of the load about X increases
D The magnitude of the vertical component of the reaction at X increases
