Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is $0.15$ ($g=10\ ms^{-2}$).

A $50\ ms^{-2}$

B $1.2\ ms^{-2}$

C $150\ ms^{-2}$

D $1.5\ ms^{-2}$

The answer is D.

Solution

In the car's frame, $f=ma\le\mu N=\mu mg$, so $a_{max}=1.5\ ms^{-2}$.

In the frame of the car: $N=mg$ and $f=ma$ $f\le\mu N\Rightarrow a\le\mu g\Rightarrow a\le1.5\ ms^{-2}$ or $a_{max}=1.5\ ms^{-2}$

Concept maximum acceleration without slipping

72 questions from this chapter have appeared across 27 exam years.