Forces and elasticity

A weight of 2 N is suspended from a spring of spring constant 50 N m^–1.

What is the elastic strain energy stored by the spring in joules?

A student stretched a length of nylon fishing line using the apparatus shown below.

The nylon fishing line was stretched by adding masses to the mass holder. The positions of the bottom of the mass holder were measured as masses were added. For each mass, the extension of the nylon fishing line was calculated. The student recorded the results, as shown in the table.

Criticise the recording of these results.

Describe how the extension of the nylon fishing line could have been determined as accurately as possible.

The strain for the nylon fishing line at its yield point is 0.04

State what is meant by yield point.

The original length of the nylon fishing line was 2.00 m.

Determine whether the fishing line was stretched beyond its yield point.

The suspension system in a car includes a spring attached to each wheel as shown.

The car, of mass 1100 kg, is stationary. Each spring is compressed by 152 mm due to a quarter of the weight of the car. Each spring is well within both the limit of proportionality and the elastic limit.

State what is meant by within the elastic limit.

Show that the stiffness of each spring is about 18 000 N m^–1.

A force is applied to the car which results in a further small compression of each spring. The force is then removed, and the body of the car oscillates with simple harmonic motion.

Determine the frequency of the oscillations.

State the conditions for simple harmonic motion.

The oscillations are heavily damped by a piston in the suspension system. The piston moves within a cylinder filled with oil, as shown. The oil has a high viscosity.

Explain why using oil of high viscosity will produce heavy damping.

A garden ornament consists of a metal flamingo suspended from a spring as shown. The spring is hung from a support using the hook.

The mass of the flamingo is 65 g. When the flamingo is suspended vertically the spring extends by 8.5 cm.

The flamingo is pulled downwards by a small extra displacement and then released. The flamingo undergoes simple harmonic motion vertically.

The instructions state that the flamingo will oscillate with a frequency of 2.5 Hz.

Deduce whether this statement is correct.

After being set into vertical oscillation, the flamingo comes to rest after a short time.

Explain why the flamingo comes to rest.

In a slight breeze the flamingo swings from side to side and behaves as a simple pendulum.

Show that the period of oscillation of the flamingo pendulum is about 2.2 s.

pendulum length = 1.25 m

The amplitude of oscillation of the flamingo pendulum is 7.5 cm.

Calculate the maximum velocity of the flamingo pendulum.

Questions 3 and 4 refer to the following information.

A horizontal force F is applied to a horizontal spring, fixed at one end.

The stiffness of the spring is k and the elastic strain energy stored is E.

A second, identical spring is added and the same force is applied to the combination of springs, as shown.

3 What is the stiffness of the combination of springs?

Questions 3 and 4 refer to the following information.

A horizontal force F is applied to a horizontal spring, fixed at one end.

The stiffness of the spring is k and the elastic strain energy stored is E.

A second, identical spring is added and the same force is applied to the combination of springs, as shown.

4 What is the elastic strain energy stored for the combination of springs?

When a force F is applied to a spring with stiffness k, the elastic potential energy stored is E.

What is the elastic potential energy stored when a force 2F is applied to a spring with stiffness 2 k ?

A student measured the deflection of a mass attached to the end of a thin strip of metal. The strip was clamped to a bench at one end as shown.

The student varied the force on the end of the strip by changing the mass attached.

The deflection was measured each time when the mass was in its equilibrium position.

The student obtained the following graph of deflection against force.

State why the mass will oscillate with simple harmonic motion when it is displaced slightly from its equilibrium position and released.

The student then investigated the oscillations of the mass on the metal strip. The student fixed different numbers of 10 g masses to the end of the metal strip.

The student noticed that the smaller the mass the higher the frequency of the oscillations. He estimated that the maximum number of oscillations he could count was two per second. He decided that the smallest mass he should use was 50 g.

Determine whether 50 g is the smallest mass he should use.

You may assume that the system acts in the same way as a mass on a spring.

A student is experimenting with different combinations of springs and recalls that in physics it is often possible to model different physical situations in similar ways.

The student suggests that a parallel combination of springs could be a model for a parallel combination of resistors in a circuit.

Derive an expression for the effective resistance R_eff of two resistors R₁ and R₂ connected in parallel in a circuit.

Assess the validity of the student’s suggestion by considering the effective stiffness of two identical springs in parallel.

Two identical springs are arranged side by side as shown.

When a force of 20 N is applied, an extension of 8 cm is obtained.

A force of 5 N is applied to one of the springs on its own.

Which of the following is the extension obtained?

A student investigated the behaviour of a spring under tension. The spring was hung vertically with a mass holder attached.

The position of the bottom of the mass holder was recorded. The spring was stretched by adding masses to the mass holder and the new positions were recorded. The extension of the spring each time was calculated.

The student produced the following table.

Criticise the student’s table.

The student used her data to plot a graph as shown.

Determine a value for the force constant k of the spring.

Two identical springs are joined in series and a bar magnet is hung from one end as shown.

The bar magnet is displaced a small distance vertically from its equilibrium position and released.

Calculate the frequency at which the system oscillates.

mass of magnet = 120 g spring constant of each spring = 22 N m⁻¹

*(d) Identical bar magnets are suspended from identical springs, with the North pole of each magnet inside a coil of wire as shown. The two coils are connected together with conducting leads.

Magnet A is displaced so that it oscillates vertically. The North pole of magnet A moves into and out of the coil of wire with simple harmonic motion. As this motion continues, magnet B starts to oscillate. The amplitude of oscillation of magnet B increases over time.

Explain why magnet B starts to oscillate with an increasing amplitude.