Elastic strain energy & plastic deformation

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?

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 ?

Seat belts are being tested by a car manufacturer. In the test, a car moving at a steady speed of 28 m s^–1 collides with a wall and stops.

A crash-test dummy in the driving seat is wearing a seat belt made from polyester webbing. The seat belt has a cross-sectional area of 0.85 cm² and a total length of 2.0 m. A student suggests that in the collision the seat belt absorbs all the kinetic energy of the dummy.

Show that the energy per unit volume that would have to be absorbed by the seat belt is about 2 10⁸ J m^–3.

mass of dummy = 75 kg

The graph shows how stress varies with strain for the seat belt.

Show that the area under the graph represents the energy stored per unit volume in the seat belt.

Use the graph to determine whether the seat belt absorbs all the kinetic energy of the dummy from part (a).

In this collision, the maximum strain of the seat belt is 0.075