You may also like

problem icon

Cannon Balls

How high will a ball taking a million seconds to fall travel?

problem icon

Dangerous Driver?

Was it possible that this dangerous driving penalty was issued in error?

problem icon

Speedo

Investigate the relationship between speeds recorded and the distance travelled in this kinematic scenario.

Board and Spool

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

1) Suppose that the spool is rotating with an angular speed $\omega$ about a point A. The spool is a rigid body, this means that the angular speed is the same for all points. Write equations for points B and C:

$$\omega_C = \frac{v_C}{R},      \omega_B = \frac{v_B}{R + r}$$

but $\omega_B = \omega_C = \omega$ and $v_B = u$ because the board does not slip on the spool. Thus, $v_C = \frac{R}{R+r}u$. This means that the speed at which the man is approching the spool is $v = u - v_C = u -\frac{R}{R+r}u =\frac{r}{R+r}u$. This means that the time needed for the man to reach the spool is $$t = \frac{l}{v} = \frac{l(R+r)}{ru}\;.$$

 2) The man will travel $s = ut = \frac{l(R+r)}{r}$.

3) If $r = R$ then $s = 2l$.

4) Plug numbers to the equations but do not forget to change units, $t = 6.48\mathrm{s}$ and $s = 6.48\mathrm{m}$.