Deformation of solids Banker

1. (a) A spring obeys Hooke's law. A force of 4.8 N extends it by 3.2 cm. What is the spring constant of the spring?A 1.5 N m⁻¹B 15 N m⁻¹C 150 N m⁻¹D 6.7 × 10⁻³ N m⁻¹ [1]

1. (a) A spring of spring constant 250 N m⁻¹ is stretched by 6.0 cm within its limit of proportionality. What is the elastic potential energy stored in the spring?A 0.45 JB 0.90 JC 15 JD 4.5 × 10³ J [1]

A spring hangs vertically from a clamp in a school laboratory in Faisalabad. Its unstretched length is 12.0 cm. When a load of 3.0 N hangs from it, its length is 15.6 cm.

1. (a) Calculate the extension of the spring when the load is 3.0 N. [1]
2. (b) Calculate the spring constant of the spring in N m⁻¹. [2]
3. (c) State Hooke's law. [1]
4. (d) Predict the length of the spring when the load is 4.5 N. State the assumption you make. [2]

1. (a) State what is meant by the elastic limit of a material. [1]
2. (b) Distinguish between elastic deformation and plastic deformation. [2]
3. (c) A metal wire is loaded until it has passed its limit of proportionality but not its elastic limit. Describe what happens to the wire when the load is removed. [1]

A boy uses a catapult (gulel) to fire a small stone of mass 25 g. The rubber band behaves like a spring of spring constant 420 N m⁻¹ and is stretched by 0.15 m. Assume it obeys Hooke's law.

1. (a) Calculate the elastic potential energy stored in the band. [2]
2. (b) The band is released and all of this energy becomes kinetic energy of the stone. Calculate the speed of the stone as it leaves the catapult. [2]
3. (c) Suggest one reason why the actual speed is less than this value. [1]

A kitchen scale contains a spring of spring constant 2.4 × 10³ N m⁻¹ that is squashed when a 1.5 kg bag of flour is placed on the pan. The spring obeys Hooke's law. (g = 9.81 m s⁻²)

1. (a) Calculate the compression of the spring. [2]
2. (b) Calculate the elastic potential energy stored in the spring. [2]
3. (c) State the type of deformation of the spring (tensile or compressive). [1]

A spring stores 0.20 J of elastic potential energy when its extension is 2.0 cm. It obeys Hooke's law over the whole range used.

1. (a) Calculate the spring constant. [2]
2. (b) Calculate the energy stored when the extension is 5.0 cm. [2]

1. (a) Which statement describes plastic deformation of a metal wire?A The wire returns to its original length when the load is removed.B The wire does not return to its original length when the load is removed.C The extension is proportional to the load.D It happens only for loads below the limit of proportionality. [1]

A copper wire is stretched in a testing machine. The force–extension graph is a straight line from the origin to the point (1.2 mm, 60 N), which is the limit of proportionality. The graph then curves, and the wire is loaded up to 70 N, at which point its extension is 2.5 mm. The load is then removed.

1. (a) Calculate the elastic potential energy stored in the wire at the limit of proportionality. [2]
2. (b) Calculate the gradient of the linear section in N mm⁻¹. [1]
3. (c) When the load is removed, the unloading line is straight and parallel to the original linear section. Calculate the permanent extension of the wire. [3]

A car of mass 1200 kg rests on four identical springs that share the weight equally and obey Hooke's law. When four passengers of total mass 280 kg get in, the car sinks a further 2.5 cm. (g = 9.81 m s⁻²)

1. (a) Calculate the spring constant of each spring. [2]
2. (b) Calculate the total compression of each spring from its natural length when the car and passengers are at rest. [2]
3. (c) Calculate the total elastic potential energy stored in the four springs with the passengers inside. [2]

The force–extension graph for a spring is a straight line through the origin, reaching a force of 8.0 N at an extension of 0.16 m.

1. (a) Explain why the area under a force–extension graph represents the work done in stretching the spring. [2]
2. (b) Calculate the work done in stretching the spring to an extension of 0.16 m. [1]
3. (c) The spring is then stretched further, from 0.16 m to 0.24 m, still within its limit of proportionality. Calculate the additional work done. [2]

A student loads and then unloads a thin metal wire. Her results are:Loading — load / N: 0, 10, 20, 30, 40; extension / mm: 0, 0.50, 1.00, 1.50, 2.30Unloading — load / N: 40, 30, 20, 10, 0; extension / mm: 2.30, 1.80, 1.30, 0.80, 0.30

1. (a) Use the loading results to state between which two loads the limit of proportionality lies. Explain your answer. [2]
2. (b) State whether the elastic limit has been exceeded. Give a reason. [2]
3. (c) Suggest why the unloading extensions are larger than the loading extensions at the same load. [1]

A student hangs slotted masses from a spring and measures its length L with a metre rule. The unloaded length is 50.0 mm.mass / g: 100, 200, 300, 400, 500L / mm: 89.8, 130.4, 169.9, 210.3, 249.8

1. (a) Calculate the extension of the spring when the mass is 300 g. [1]
2. (b) Using the first and last readings, calculate the spring constant k. (g = 9.81 m s⁻²) [3]
3. (c) Each length is measured with an uncertainty of ±1 mm. Calculate the percentage uncertainty in the extension for the 100 g load. [2]
4. (d) Suggest two improvements to reduce the uncertainty in the length readings. [2]

1. (a) A spring of spring constant 80 N m⁻¹ obeys Hooke's law. Its extension is increased slowly from 5.0 cm to 15.0 cm. How much work is done on the spring?A 0.40 JB 0.80 JC 0.90 JD 1.6 J [1]

A toy launcher contains a spring of spring constant 600 N m⁻¹. The spring is compressed by 4.0 cm and released, firing a ball of mass 12 g vertically upwards. (g = 9.81 m s⁻²)

1. (a) Calculate the elastic potential energy stored in the compressed spring. [2]
2. (b) Calculate the maximum height the ball could reach above its starting point, ignoring air resistance and the small change in height while the spring extends. [2]
3. (c) The ball actually rises 3.1 m. Calculate the percentage of the stored energy that is not converted to gravitational potential energy. [2]

A light spring of spring constant 40 N m⁻¹ hangs vertically. A mass of 0.50 kg is attached to its lower end. The spring obeys Hooke's law throughout. (g = 9.81 m s⁻²)

1. (a) The mass is lowered gently by hand until it hangs at rest. Calculate the extension of the spring. [1]
2. (b) For the lowering in (a), calculate (i) the gravitational potential energy lost by the mass and (ii) the elastic potential energy gained by the spring. [2]
3. (c) Explain the difference between the two energies in (b). [1]
4. (d) The mass is now instead attached at the natural length and released from rest. Calculate the maximum extension of the spring. [2]

A wide rubber exercise band is stretched and the following readings are taken:extension / cm: 0, 2.0, 4.0, 6.0, 8.0, 10.0force / N: 0, 1.4, 2.2, 2.6, 3.0, 3.8

1. (a) State how the data show that the band does not obey Hooke's law. [1]
2. (b) Use the trapezium rule to estimate the work done in stretching the band to an extension of 10 cm. [3]
3. (c) A student calculates the energy as ½ × 3.8 N × 0.10 m. State the value obtained and explain why it is not valid here. [2]

1. (a) A student suggests that the spring constant k of a helical spring depends on the number N of turns in the spring, and that k = c/N where c is a constant. Design a laboratory experiment to test the relationship between k and N. Explain how your results could be used to test the relationship and to find c. Describe the arrangement in words (no diagram is needed) and include: the procedure, including how N is changed and k is measured; the control of variables; the analysis of data; any safety precautions. [15]

A buffer spring at the bottom of a lift shaft has spring constant 1.8 × 10⁵ N m⁻¹. In a safety test a lift car of mass 900 kg, moving downwards at 1.5 m s⁻¹, lands on the spring. Ignore friction, air resistance and the mass of the spring. The spring obeys Hooke's law. (g = 9.81 m s⁻²)

1. (a) Explain why the maximum compression is not found simply from ½mv² = ½kx². [1]
2. (b) Show that at maximum compression x, ½kx² = ½mv² + mgx. [1]
3. (c) Calculate the maximum compression of the buffer. [3]
4. (d) Calculate the maximum force exerted by the buffer on the lift. [1]

1. (a) What are the SI base units of the Young modulus?A kg m s⁻²B kg m⁻¹ s⁻²C kg m⁻² s⁻²D kg s⁻² [1]

1. (a) Define stress and strain. [2]
2. (b) Define the Young modulus. [1]
3. (c) A nylon fishing line of diameter 0.40 mm holds a fish with a tension of 25 N. Calculate the stress in the line. [2]

A steel crane cable at a container port in Karachi has a diameter of 2.0 cm and a length of 30 m. It supports a container with a tension of 4.0 × 10⁴ N. The Young modulus of steel is 2.1 × 10¹¹ Pa.

1. (a) Calculate the stress in the cable. [2]
2. (b) Calculate the strain in the cable. [1]
3. (c) Calculate the extension of the cable. [1]

A student plans to determine the Young modulus of copper using a long, thin copper wire clamped at one end, passing over a pulley, with masses hung on the free end.

1. (a) Describe the measurements needed and the instrument used for each. [4]
2. (b) Explain how a graph of the results is used to find the Young modulus. [2]

1. (a) A steel wire of length 2.5 m and diameter 0.80 mm has Young modulus 2.0 × 10¹¹ Pa. What tension produces an extension of 1.0 mm?A 10 NB 40 NC 160 ND 4.0 × 10⁴ N [1]

A steel wire of length 1.5 m is joined end-to-end to a copper wire of length 1.0 m. Both wires have diameter 0.60 mm. The combined wire hangs vertically and supports a load of 60 N. Young modulus: steel 2.0 × 10¹¹ Pa, copper 1.2 × 10¹¹ Pa. Both wires obey Hooke's law.

1. (a) Explain why the tension is the same in both wires. [1]
2. (b) Calculate the extension of the steel wire. [2]
3. (c) Calculate the total extension of the combined wire. [2]

An aluminium wire of length 2.0 m and cross-sectional area 1.5 mm² supports a load of 90 N. The Young modulus of aluminium is 7.0 × 10¹⁰ Pa. The wire obeys Hooke's law.

1. (a) Calculate the extension of the wire. [2]
2. (b) Calculate the elastic potential energy stored in the wire. [2]
3. (c) The aluminium wire is replaced by a wire of the same material and length but with twice the cross-sectional area. The same load is applied. State the new energy stored. [1]

1. (a) Wires X and Y are made of the same metal. Wire Y has twice the length and twice the diameter of wire X. The same tension, below the limit of proportionality, is applied to each. What is the ratio (extension of Y) ÷ (extension of X)?A ¼B ½C 1D 2 [1]

A tensile test on a metal sample gives these results:strain: 0, 0.0010, 0.0020, 0.0030, 0.0040, 0.0060stress / MPa: 0, 70, 140, 210, 250, 270

1. (a) Determine the Young modulus of the material. [2]
2. (b) State the approximate stress at the limit of proportionality. [1]
3. (c) A wire of this material has diameter 1.2 mm. Calculate the maximum load it can support without exceeding the limit of proportionality. [2]
4. (d) The wire in (c) has length 3.0 m. Calculate its extension at this load. [1]

A uniform copper wire of length 2.0 m has a mass of 8.9 g. The density of copper is 8900 kg m⁻³. A load of 40 N produces an extension of 1.33 mm, within the limit of proportionality.

1. (a) Show that the cross-sectional area of the wire is 5.0 × 10⁻⁷ m². [2]
2. (b) Calculate the Young modulus of copper from these results. [2]
3. (c) Calculate the elastic potential energy stored in the wire. [1]
4. (d) Explain why measuring the mass and length is a more accurate way to find the area of this wire than measuring its diameter with a micrometer. [1]

In an experiment to find the Young modulus of steel, a wire of length 2.40 m is loaded. Three micrometer readings of the diameter are 0.42 mm, 0.43 mm and 0.41 mm.load / N: 0, 10, 20, 30, 40, 50extension / mm: 0, 0.87, 1.73, 2.61, 3.46, 4.33

1. (a) Calculate the mean diameter and the cross-sectional area of the wire. [2]
2. (b) Use the first and last readings to find the gradient of a graph of load against extension, and hence determine the Young modulus. [3]
3. (c) The micrometer reads to ±0.01 mm. Calculate the percentage uncertainty in the cross-sectional area. [2]
4. (d) Explain why a long, thin wire is used. [1]