6.1. Stress and strain
A subsection of Physics, 9702, through 6. Deformation of solids
Listing 10 of 226 questions
The variation with extension x of the force F acting on a spring is shown in . 1.0 2.0 3.0 4.0 5.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 x / m F / N The spring of unstretched length 0.40 m has one end attached to a fixed point, as shown in . 0.40 m unstretched spring 0.72 m block moving downwards block, weight 2.5 N A block of weight 2.5 N is then attached to the spring. The block is then released and begins to move downwards. At one instant, as the block is continuing to move downwards, the spring has a length of 0.72 m, as shown in . Assume that the air resistance and the mass of the spring are both negligible. For the change in length of the spring from 0.40 m to 0.72 m: use to show that the increase in elastic potential energy of the spring is 0.64 J calculate the decrease in gravitational potential energy of the block of weight 2.5 N. decrease in potential energy = J Use the information in and your answer in to determine, for the instant when the length of the spring is 0.72 m: the kinetic energy of the block kinetic energy = J the speed of the block. speed = m s−1
9702_s19_qp_21
THEORY
2019
Paper 2, Variant 1
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Define the moment of a force about a point. shows a type of balance that is used for measuring mass. fixed point P spring pan pivot rod pointer 52.6 cm 1.8 cm 6.2 cm mm scale (not to scale) A rigid rod is pivoted about a point 6.2 cm from the centre of a pan which is attached to one end. The object being measured is placed on the centre of this pan. A spring, attached to the rod 1.8 cm from the pivot, is attached at its other end to a fixed point P. The spring obeys Hooke’s law over the full range of operation of the balance. A pointer, on the other side of the pivot, is set against a millimetre scale which is a distance 52.6 cm from the pivot. When the system is in equilibrium with no mass on the pan, the rod is horizontal and the pointer indicates a reading on the scale of 86 mm. An object of mass 0.472 kg is now placed on the pan. As a result, the pointer moves to indicate a reading of 123 mm on the scale when the system is again in equilibrium. Show that the increase in the length of the spring is approximately 1.3 mm. Calculate the magnitude of the moment about the pivot of the weight of the object. moment = N m Use your answer in to determine the increase in the tension in the spring due to the 0.472 kg mass. increase in tension = N Use the information in and your answer in to determine the spring constant k of the spring. Give a unit with your answer. k = unit
9702_s21_qp_23
THEORY
2021
Paper 2, Variant 3
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A sphere is attached by a metal wire to the horizontal surface at the bottom of a river, as shown in . 68° direction of flow of water wire sphere water horizontal surface (not to scale) The sphere is fully submerged and in equilibrium, with the wire at an angle of 68° to the horizontal surface. The weight of the sphere is 32 N. The upthrust acting on the sphere is 280 N. The density of the water is 1.0 × 103 kg m–3. Assume that the force on the sphere due to the water flow is in a horizontal direction. By considering the components of force in the vertical direction, determine the tension in the wire. tension = N For the sphere, calculate: the volume volume = m3 the density. density = kg m–3 The centre of the sphere is initially at a height of 6.2 m above the horizontal surface. The speed of the water then increases, causing the sphere to move to a different position. This movement of the sphere causes its gravitational potential energy to decrease by 77 J. Calculate the final height of the centre of the sphere above the horizontal surface. height = m The extension of the wire increases when the sphere changes position as described in . The wire obeys Hooke’s law. State a symbol equation that gives the relationship between the tension T in the wire and its extension x. Identify any other symbol that you use. Before the sphere changed position, the initial elastic potential energy of the wire was 0.65 J. The change in position of the sphere causes the extension of the wire to double. Calculate the final elastic potential energy of the wire after the sphere has changed position. final elastic potential energy = J
9702_s22_qp_22
THEORY
2022
Paper 2, Variant 2
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A rigid uniform beam of weight W is connected to a fixed support by a hinge, as shown in . string horizontal ground fixed support hinge beam 0.50 m 0.10 m 0.20 m 0.40 m 0.30 N 4.8 N 30° spring W (not to scale) A compressed spring exerts a total force of 8.2 N vertically upwards on the horizontal beam. A block of weight 0.30 N rests on the beam. The right‑hand end of the beam is connected to the ground by a string at an angle of 30° to the horizontal. The tension in the string is 4.8 N. The distances along the beam are shown in . The beam is in equilibrium. Assume that the hinge is frictionless. Show that the vertical component of the tension in the string is 2.4 N. By taking moments about the hinge, determine the weight W of the beam. W = N Calculate the horizontal component of the force exerted on the beam by the hinge. force = N The spring obeys Hooke’s law and has an elastic potential energy of 0.32 J. Calculate the compression of the spring. compression = m The string is cut so that the spring extends upwards. This causes the beam to rotate and launch the block into the air. The block reaches its maximum height and then falls back to the ground. shows part of the path of the block in the air shortly before it hits the horizontal ground. 0.090 m horizontal ground path of block B A (not to scale) The block is at a height of 0.090 m above the ground when it passes through point A. The block has a kinetic energy of 0.044 J when it hits the ground at point B. Air resistance is negligible. Calculate the decrease in the gravitational potential energy of the block for its movement from A to B. decrease in gravitational potential energy = J Use your answer in and conservation of energy to determine the speed of the block at point A. speed = m s–1 By reference to the force on the block, explain why the horizontal component of the velocity of the block remains constant as it moves from A to B. The block passes through point A at time tA and arrives at point B at time tB. On , sketch a graph to show the variation of the magnitude of the vertical component vY of the velocity of the block with time t from t = tA to t = tB. Numerical values of vY are not required. tA vY tB t
9702_s23_qp_21
THEORY
2023
Paper 2, Variant 1
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A spring is suspended from a fixed point at one end. The spring is extended by a vertical force applied to the other end. The variation of the applied force F with the length L of the spring is shown in . L / cm F / N For the spring: state the name of the law that gives the relationship between the force and the extension determine the spring constant, in N m–1 spring constant = N m–1 determine the elastic potential energy when F = 6.0 N. elastic potential energy = J
9702_s23_qp_22
THEORY
2023
Paper 2, Variant 2
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Questions Discovered
226