6. Deformation of solids
A section of Physics, 9702
Listing 10 of 301 questions
A hot-air balloon floats just above the ground. The balloon is stationary and is held in place by a vertical rope, as shown in . balloon rope ground The balloon has a weight W of 3.39 × 104 N. The tension T in the rope is 4.00 × 102 N. Upthrust U acts on the balloon. The density of the surrounding air is 1.23 kg m–3. On , draw labelled arrows to show the directions of the three forces acting on the balloon. Calculate the volume, to three significant figures, of the balloon. volume = m3 The balloon is released from the rope. Calculate the initial acceleration of the balloon. acceleration = m s–2 The balloon is stationary at a height of 500 m above the ground. A tennis ball is released from rest and falls vertically from the balloon. A passenger in the balloon uses the equation v2 = u2 + 2as to calculate that the ball will be travelling at a speed of approximately 100 m s–1 when it hits the ground. Explain why the actual speed of the ball will be much lower than 100 m s–1 when it hits the ground. Before the balloon is released, the rope holding the balloon has a strain of 2.4 × 10–5. The rope has an unstretched length of 2.5 m. The rope obeys Hooke’s law. Show that the extension of the rope is 6.0 × 10–5 m. Calculate the elastic potential energy EP of the rope. EP = J The rope holding the balloon is replaced with a new one of the same original length and cross-sectional area. The tension is unchanged and the new rope also obeys Hooke’s law. The new rope is made from a material of a lower Young modulus. State and explain the effect of the lower Young modulus on the elastic potential energy of the rope.
9702_w23_qp_21
THEORY
2023
Paper 2, Variant 1
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A vertical rod is fixed to the horizontal surface of a table, as shown in . rod spring surface of table (not to scale) A spring of mass 7.5 g is able to slide along the full length of the rod. The spring is first pushed against the surface of the table so that it has an initial compression of 2.1 cm. The spring is then suddenly released so that it leaves the surface of the table with a kinetic energy of 0.048 J and then moves up the rod. Assume that the spring obeys Hooke’s law and that the initial elastic potential energy of the compressed spring is equal to the kinetic energy of the spring as it leaves the surface of the table. Air resistance is negligible. By using the initial elastic potential energy of the compressed spring, calculate its spring constant. spring constant = N m–1 Calculate the speed of the spring as it leaves the surface of the table. speed = m s–1 The spring rises to its maximum height up the rod from the surface of the table. This causes the gravitational potential energy of the spring to increase by 0.039 J. Calculate, for this movement of the spring, the increase in height of the spring after leaving the surface of the table. increase in height = m Calculate the average frictional force exerted by the rod on the spring as it rises. average frictional force = N The rod is replaced by another rod that exerts negligible frictional force on the moving spring. The initial compression x of the spring is now varied in order to vary the maximum increase in height Δh of the spring after leaving the surface of the table. Assume that the spring obeys Hooke’s law for all compressions. On , sketch a graph to show the variation with x of Δh. Numerical values are not required. Δh x
9702_w23_qp_22
THEORY
2023
Paper 2, Variant 2
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State what is meant by work done, elastic potential energy. A block of mass 0.40 kg slides in a straight line with a constant speed of 0.30 m s−1 along a horizontal surface, as shown in . 0.30 m s–1 block mass 0.40 kg spring The block hits a spring and decelerates. The speed of the block becomes zero when the spring is compressed by 8.0 cm. Calculate the initial kinetic energy of the block. kinetic energy = J The variation of the compression x of the spring with the force F applied to the spring is shown in . 8.0 x / cm FMAX F Use your answer in to determine the maximum force FMAX exerted on the spring by the block. Explain your working. FMAX = N Calculate the maximum deceleration of the block. deceleration = m s−2 State and explain whether the block is in equilibrium 1. before it hits the spring, 2. when its speed becomes zero. The energy E stored in a spring is given by E = 1 2 k x 2 where k is the spring constant of the spring and x is its compression. The mass m of the block in is now varied. The initial speed of the block remains constant and the spring continues to obey Hooke’s law. On , sketch the variation of the maximum compression x0 of the spring with mass m. x0 m
9702_m16_qp_22
THEORY
2016
Paper 2, Variant 2
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Describe, with a labelled diagram, the structure of a metal-wire strain gauge. In a strain gauge, the increase in resistance ΔR depends on the increase in length ΔL. The variation of ΔR with ΔL is shown in . ΔL / 10–5 m ΔR / Ω The strain gauge is connected into a circuit incorporating an ideal operational amplifier (op-amp), as shown in . – + strain gauge +2.00 V +5 V –5 V A 0 V 153.0 Ω +6.00 V X Y The strain gauge is initially unstrained with resistance 300.0 Ω. Use data from to calculate the increase in length ΔL of the strain gauge that gives rise to a potential of +2.00 V at point A in . ΔL = ……………………………….m The strain gauge undergoes a further increase in length beyond the value in . State and explain which one of the light-emitting diodes, X or Y, will be emitting light.
9702_m17_qp_42
THEORY
2017
Paper 4, Variant 2
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For the deformation of a wire under tension, define stress, strain. A wire is fixed at one end so that it hangs vertically. The wire is given an extension x by suspending a load F from its free end. The variation of F with x is shown in . 0.1 0.2 0.3 0.4 x / mm F / N 0.5 0.6 0.7 0.8 The wire has cross-sectional area 9.4 × 10–8 m2 and original length 2.5 m. Describe how measurements can be taken to determine accurately the cross-sectional area of the wire. Determine the Young modulus E of the material of the wire. E = Pa Use to calculate the increase in the energy stored in the wire when the load is increased from 2.0 N to 4.0 N. increase in energy = J The wire in is replaced by a new wire of the same material. The new wire has twice the length and twice the diameter of the old wire. The new wire also obeys Hooke’s law. On , sketch the variation with extension x of the load F for the new wire from x = 0 to x = 0.80 mm.
9702_m18_qp_22
THEORY
2018
Paper 2, Variant 2
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Questions Discovered
301