Question

In this figure the force should be applied on mass m = 5kg so that it just won't slip is(Given that car is moving with constant acceleration a = 5m/s and coefficient of friction is 0.4)

Answer 1

Given:

The car is moving with constant acceleration a = 5m/s and coefficient of friction is 0.4.

To find:

Force applied to mass m.

Calculation:

Let net force needed be F ;

Now , the friction on mass m should balance its weight:

$\therefore \: \rm{f = mg}$

$= > \rm{ \mu N = mg}$

$= > \rm{ (0.4) N = 5 \times 10}$

$= > \rm{ (0.4) N = 50}$

$= > \rm{N = \dfrac{50}{0.4}}$

$= > \rm{N = 125 \: newton}$

Now , the required force as per FBD:

$\therefore \: \rm{F - N \: = ma}$

$= > \: \rm{F - 125 = 5 \times 5}$

$= > \: \rm{F - 125 = 25}$

$= > \: \rm{F = 125 + 25}$

$= > \: \rm{F = 150 \: newton}$

So, final answer is:

$\boxed{\: \rm{F = 150 \: newton}}$