Question

A truck is traveling on a level road. The driver suddenly applies the brakes, causing the truck to decelerate by an amount g/2. This causes a box in the rear of the truck to slide forward. If the coefficient of sliding friction between the box and the truckbed is 2/5, find the acceleration of the box relative to the truck and relative to the road.

Answer 1

Answer:

Truck $\dfrac{g}{10}$

Road $-\dfrac{g}{10}$

Explanation:

$a_1$ = Acceleration of truck = $-\dfrac{g}{2}$

$\mu$ = Coefficient of friction = $\dfrac{2}{5}$

Frictional force is given by

$f=-\mu mg\\\Rightarrow f=-\dfrac{2}{5}mg\\\Rightarrow ma_2=-\dfrac{2}{5}mg\\\Rightarrow a_2=-\dfrac{2}{5}g$

Net acceleration is given by

$a=a_2-a_1\\\Rightarrow a=-\dfrac{2}{5}g+\dfrac{g}{2}\\\Rightarrow a=\dfrac{g}{10}$

The acceleration of the box relative to the truck is $\dfrac{g}{10}$ and $-\dfrac{g}{10}$ relative to the road.