The way the tension $F$ in a spring changes with extension $x$ is shown in Fig. 3.1. Use Fig. 3.1 to calculate the energy stored in the spring when the extension is $4.0\,\text{cm}$. Show your working.
Explain why, as the spring’s extension decreases, the momentum of trolley A is equal in magnitude but opposite in direction to the momentum of trolley B.
At the moment when the extension of the spring is zero, trolley A has speed $V_1$ and trolley B has speed $V_2$. Write down a momentum equation that links $V_1$ and $V_2$.
Write down an equation that links the initial energy $E$ stored in the spring to the final energies of the trolleys.
Show that the kinetic energy $E_K$ of an object of mass $m$ is linked to its momentum $p$ by $E_K = \frac{p^2}{2m}$.
Trolley A has a greater mass than trolley B. Use your answer in (ii) part 1 to deduce which trolley, A or B, has the greater kinetic energy at the instant when the spring’s extension is zero.
Show that the kinetic energy $E_{K}$ of an object of mass $m$ is related to its momentum $p$ by $E_{K} = \frac{p^{2}}{2m}$.
Trolley A has a greater mass than trolley B. Use your answer in (ii) part 1 to deduce which trolley, A or B, has the greater kinetic energy at the instant when the spring’s extension is zero.