Question

Fig. 2.1 shows a train
Fig. 2.1
The total mass of the train and its passengers is 750000kg. The train is travelling at a speed of 84m/s.
The driver applies the brakes and the train takes 80s to slow down to a speed of 42m/s.
(a) Calculate the impulse applied to the train as it slows down,
impulse =
[3]
(b) Calculate the average resultant force applied to the train as it slows down,
force =
(2)

Answer 1

Answer:

$\mathrm{(a)\:}32,000,000\:\mathrm{Ns},\\\mathrm{(b)\:}390,000\:\mathrm{N}$

Explanation:

The impulse-momentum theorem states the impulse on an object is equal to the change in momentum of that object. Momentum is given by $p=mv$. Since mass is constant, the train's change in momentum is:

$\Delta p=m\Delta v=750,000\cdot42=31,500,000=\fbox{ 32,000,000\:\mathrm{Ns} }$(two significant figures).

Impulse is also given as $\Delta p = F\Delta t$, where $F$ is the average force applied and $\Delta t$ is change in time. Since $t$ is given as $80\mathrm{s}$, we have the following equation:

$F\Delta t=\Delta p\\\\F=\frac{\Delta p}{\Delta t},\\\\F=\frac{31,500,000}{80},\\\\F=393,750=\fbox{ 390,000\:\mathrm{N} }$(two significant figures).