- #1

- 11

- 0

## Homework Statement

A rocket Propelled Trolly begins at rest time

*t = 0s,*and then accelerates along a straight track such that the speed at time

*t*is

[itex]v(t)=bt^{2}[/itex]

where

*b*is a constant, during the period

*0<t<t*. at time [itex]t_{2}[/itex], the rocket fuel is exhausted and the trolley continues with constant speed

_{2}[itex]v_{f}=bt^{2}_{2}[/itex]

A coin is initially at rest on the floor of the trolley. At time [itex]t_{1}[/itex], where [itex]0<t_{1}<t_{2}[/itex], it starts to slide backwards. It stops sliding at [itex]t_{3}[/itex], where [itex]t_{3}>t_{2}[/itex].

Use this information to obtain expressions for the coefficients of static and kinetic friction between the coin and the floor of the trolley.

**2. The attempt at a solution**

[itex]a=\frac{d}{dt}(v(t))[/itex]

[itex]a=2bt[/itex]

[itex]F_{s}=\mu_{2}N[/itex]

[itex]F_{s}=Ma[/itex] (M=mass of trolley)

[itex]N=mg[/itex] (m=mass of coin)

[itex]\mu_{s}=\frac{F_{s}}{N}[/itex]

[itex]\mu_{s}=\frac{2btM}{mg}[/itex]

Thats as far as I got and I'm not even sure if what I've done is correct.

Thanks in advance.