6. Deformation of solids
A section of Physics, 9702
Listing 10 of 301 questions
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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The variation of stress with strain for a metal P is shown in . 0.5 1.0 1.5 strain (%) stress / 107 Pa E Point E is the elastic limit of the metal. Use to determine the Young modulus for P. Young modulus = Pa On the line in , draw a cross (×) to show the limit of proportionality. Label this point Q. State the conditions necessary for an object to be in equilibrium. A wire is used to hold a uniform shelf AB horizontally in equilibrium as shown in . wire wall hinge 0.65 m shelf 0.12 m cup B A 50° (not to scale) The wire is connected to the midpoint of shelf AB at an angle of 50° to the horizontal. The shelf is attached to a wall by a hinge at A. The length of shelf AB is 0.65 m and its weight is 33 N. A cup of weight 1.5 N rests on the shelf with its centre of gravity at a horizontal distance of 0.12 m from B. By taking moments about A, determine the tension in the wire. tension = N The stress in the wire is 1.5 × 107 Pa. Determine the radius of the wire. radius = m More items are added to the shelf, doubling the stress in the wire. The wire is made of the metal P from . Use to state and explain whether the wire will behave plastically or elastically as the stress doubles.
9702_w24_qp_22
THEORY
2024
Paper 2, Variant 2
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Define the terms 1. tensile stress, 2. tensile strain, 3. the Young modulus. Suggest why the Young modulus is not used to describe the deformation of a liquid or a gas. The change ∆V in the volume V of some water when the pressure on the water increases by ∆p is given by the expression ∆p = 2.2 × 109 ∆V V , where ∆p is measured in pascal. In many applications, water is assumed to be incompressible. By reference to the expression, justify this assumption. Normal atmospheric pressure is 1.01 × 105 Pa. Divers in water of density 1.08 × 103 kg m–3 frequently use an approximation that every 10 m increase in depth of water is equivalent to one atmosphere increase in pressure. Determine the percentage error in this approximation. error = %
9702_s08_qp_2
THEORY
2008
Paper 2, Variant 0
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Questions Discovered
301