6.1. Stress and strain
A subsection of Physics, 9702, through 6. Deformation of solids
Listing 10 of 226 questions
A steel ball is projected horizontally from the top of a table, as shown in . table 180 cm ground edge of table ball path of ball 4.9 m s–1 (not to scale) The ball is projected horizontally at a speed of 4.9 m s–1. The ball lands on the ground a horizontal distance of 180 cm from the edge of the table. Assume that air resistance is negligible. Calculate the time taken for the ball to reach the ground. time = s Calculate the vertical component of the velocity of the ball as it hits the ground. velocity = m s–1 Determine the magnitude and the angle to the horizontal of the velocity of the ball as it hits the ground. magnitude of velocity = m s–1 angle to the horizontal = ° The ball is projected by means of a compressed spring which is attached to a fixed block as shown in . x0 ball spring frictionless track fixed block The ball is placed on a frictionless track in front of the spring. The ball is then pulled back so that the spring has compression x0. When the spring is released, the ball is projected horizontally as shown in . ball spring The variation with compression x of the applied force F for the spring is shown in . x / cm F / N The ball is a uniform sphere of steel of diameter 0.016 m and mass 0.017 kg. Calculate the density of the steel. density = kg m–3 All of the elastic potential energy in the spring is converted into kinetic energy of the ball. The speed of the ball as it leaves the spring is 4.9 m s–1. Show that the maximum elastic potential energy of the spring is 0.20 J. Use to determine the spring constant k of the spring. k = N m–1 Use your answer in and the value of energy given in to determine the compression x0 of the spring. x0 = m The steel ball is replaced by a polystyrene ball of the same diameter but of much lower mass. The spring is given compression x0 and is then released. Air resistance on this ball is not negligible after it leaves the spring. Explain: why this ball leaves the spring with a greater speed than that of the steel ball why this ball takes a longer time to reach the ground than the steel ball.
9702_w22_qp_21
THEORY
2022
Paper 2, Variant 1
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State what is meant by the centre of gravity of an object. A uniform beam AB is attached by a frictionless hinge to a vertical wall at end A. The beam is held so that it is horizontal by a metal wire CD, as shown in . 45 N 37° D wire block B 23 N W 0.56 m 0.20 m 0.20 m wall hinge C A (not to scale) The beam is of length 0.96 m and weight 23 N. A block of weight W rests on the beam at a distance of 0.20 m from end B. The wire is attached to the beam at point D which is a distance of 0.40 m from end B. The wire exerts a force on the beam of 45 N at an angle of 37° to the horizontal. The beam is in equilibrium. Calculate the vertical component of the force exerted by the wire on the beam. vertical component of the force = N By taking moments about A, calculate the weight W of the block. W = N The hinge exerts a force on the beam at end A. Calculate the horizontal component of this force. horizontal component of force = N The block is now placed closer to point D on the beam. State whether this change will increase, decrease or have no effect on the tension in the wire. The stress in the wire is 5.3 × 107 Pa. The wire is now replaced by a second wire that has a radius which is three times greater than that of the original wire. The tension in the wire is unchanged. Calculate the stress in the second wire. stress = Pa
9702_w22_qp_22
THEORY
2022
Paper 2, Variant 2
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A horizontal spring is fixed at one end. A block is pushed against the other end of the spring so that the spring is compressed, as shown in . compressed spring block frictionless surface The block is released and accelerates along a horizontal frictionless surface as the spring returns to its original length. The block leaves the end of the spring with a speed of 2.3 m s–1, as shown in . spring block leaving the spring speed 2.3 m s–1 The block has a mass of 250 g and the spring has a spring constant of 420 N m–1. Assume that the spring always obeys Hooke’s law and that all the elastic potential energy of the spring is transferred to the kinetic energy of the block. Calculate the kinetic energy of the block as it leaves the spring. kinetic energy = J Calculate the compression of the spring immediately before the block is released. compression = m After leaving the spring, the block moves along the surface until it hits a barrier at a speed of 2.3 m s–1. The block then rebounds at a speed of 1.5 m s–1 and moves back along its original path. The block is in contact with the barrier for a time of 0.086 s. Calculate: the change in momentum of the block during the collision change in momentum = N s the average resultant force exerted on the block during the collision. average resultant force = N The maximum compression x of the spring is now varied in order to vary the kinetic energy EK of the block as it leaves the spring. Assume that all the elastic potential energy in the spring is always transferred to the kinetic energy of the block. On , sketch a graph to show the variation with x of EK. EK x
9702_w22_qp_22
THEORY
2022
Paper 2, Variant 2
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State the principle of moments. A hollow plastic sphere is attached at one end of a bar. The sphere is partially submerged in water and the bar is attached to a fixed vertical support by a pivot P, as shown in . 40° bar fixed support P sphere, weight 0.30 N 0.29 m surface of water (not to scale) The sphere has weight 0.30 N. The distance from P to the centre of gravity of the sphere is 0.29 m. Assume that the weight of the bar is negligible. Calculate the moment of the weight of the sphere about P. moment = N m The system shown in is part of a mechanism that controls the amount of water in a tank. Water enters the tank and causes the sphere to rise. This results in the bar becoming horizontal. shows the system in its new position. P 0.29 m 0.017 m spring R submerged portion of sphere water (not to scale) In this position the rod R exerts a force to compress a horizontal spring that controls the water supply to the tank. R is positioned at a perpendicular distance of 0.017 m above P. The variation of the force F applied to the spring with compression x of the spring is shown in . x / mm F / N Use to calculate the spring constant k of the spring. k = N m–1 At the position shown in , the system is stationary and in equilibrium. The radius of the sphere is 0.0480 m and 26.0% of the volume of the sphere is submerged. The density of water is 1.00 × 103 kg m–3. Show that the upthrust on the sphere is 1.18 N. By taking moments about P, determine the force exerted on the spring by the rod R. force = N Calculate the elastic potential energy EP of the compressed spring. EP = J When the sphere moves from the position shown in to the position shown in , the upthrust on the sphere does work. Assume that resistive forces are negligible. Explain why the work done by the upthrust is not equal to the gain in elastic potential energy of the spring.
9702_w22_qp_23
THEORY
2022
Paper 2, Variant 3
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shows the variation with extension x of the tensile force F for two wires, G and H, made from the same material. 0.1 0.2 0.3 0.4 0.5 0.6 0.5 1.0 1.5 2.0 2.5 3.0 3.5 F / N x / mm G H The elastic limit has not been exceeded for G or H. For the lines in : state what is represented by the gradient explain why the area under the line represents the elastic potential energy of the wire. Wires G and H are joined together end‑to‑end to form a composite wire of negligible weight. The composite wire hangs vertically from a fixed support. A block of weight of 2.0 N is attached to the end of the wire, as shown in . G H fixed support block, weight 2.0 N Use to determine: ● the extension xG of wire G xG = mm ● the extension xH of wire H. xH = mm Calculate the total elastic potential energy EP of the composite wire due to the weight of the block. EP = J The original length of wire G is L and the original length of wire H is 1.5 L. Calculate the ratio cross‑sectional area of wire G cross‑sectional area of wire H. ratio =
9702_w23_qp_23
THEORY
2023
Paper 2, Variant 3
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Questions Discovered
226