Physics 9702 · AS & A Level · Energy conservation

Energy conservation — practice question

A spring is suspended vertically from a fixed point, and a 94 g mass is attached to it, stretching the spring as shown in Fig. 5.1. The mass is lifted vertically until the spring is at its unextended length, as shown in Fig. 5.2. The mass is then let go. It travels a vertical distance of $2.6\,\text{cm}$ before momentarily stopping, as shown in Fig. 5.3.
(a(i))[1]

State which diagram, Fig. 5.1, Fig. 5.2 or Fig. 5.3, shows the mass in the position where it has maximum gravitational potential energy.

(a(ii))[1]

State which diagram, Fig. 5.1, Fig. 5.2 or Fig. 5.3, shows the mass in the position where the spring has maximum strain energy.

(b)[1]

Briefly describe how the kinetic energy of the mass varies as the mass falls from its highest position (Fig. 5.2) to its lowest position (Fig. 5.3).

(c(i))[2]

The strain energy $E$ stored in the spring is described by the expression $E = \tfrac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the extension of the spring. For the mass moving between the positions shown in Fig. 5.2 and Fig. 5.3, calculate the change in the gravitational potential energy of the mass.

(c(ii))[3]

Determine the extension of the spring at which the strain energy is half its maximum value.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct diagram is Fig. 5.2.” …

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