Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
The track $ABCD$ is shown lying in a vertical plane. $AB$ is a straight smooth slope at an angle of $30^\circ$ to the horizontal, $BC$ is a horizontal rough straight section, and $CD$ is another rough straight slope at an angle of $30^\circ$ to the horizontal. Each of $AB$, $BC$ and $CD$ has length $2\,\text{m}$. A particle is let go from rest at $A$. The coefficient of friction between the particle and both $BC$ and $CD$ is $\mu$. The particle’s speed is unchanged as it goes through $B$ and also as it goes through $C$.
(a)[5]
It is stated that $\mu = 0.1$. Determine how far the particle has travelled up $CD$ when its speed is $1\,\text{m s}^{-1}$.
(b)[4]
A different value of $\mu$ is now used, and the particle moves $1\,\text{m}$ up the track from $C$ before coming to rest instantly. Find $\mu$ and the speed of the particle at the instant it passes $C$ for the second time.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Take the reaction on $CD$ to be $R=mg\cos30$” …