Question

A man of mass 80 kg is standing stationary in the middle of a train
carriage (see the figure below). The train is moving horizontally with a constant speed of
20 m/s (see the figure below), and the carriage is L = 20 m long. Suddenly, the train starts to accelerate uniformly with a = 2 m/s2 horizontally.
(a) Is the reference frame of the train now an inertial frame? Design an experiment that
allows you to find out.
(b) Draw a free-body diagram of the man. Label the forces appropriately and explain
their physical origin (one line each will suffice).
(c) If the coefficient of friction between the man’s shoes and the ‘floor’ of the train is
µ = 0.1, what is the maximum time that the man takes to hit the back of the train
carriage? For simplicity, you can assume that the coefficient of static friction is the
same as the coefficient of kinetic friction. Assume that there are no obstacles between
the man and the back of the train.

Answer 1

(a) It is not an inertial system because it moves with acceleration

(b) The force of friction counteracts the acceleration of man

(c)

We can write according to the Second Law of Newton

$µmg=ma (1)$

Using (1) we get

$a=µg (2)$

a=1 m/s2

We can write for move of man

$2as=v^2- u^2 (3)$

In our case, u=0 m/s

v=6.32 m/s

The acceleration is given by formula

$a=\frac {v-u}{t} (4)$

t=6.32 s