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

Truck
`(g)/(10)`

Road
`-(g)/(10)`

Step-by-step explanation:

`a_1` = Acceleration of truck =
`-(g)/(2)`

`\mu` = Coefficient of friction =
`(2)/(5)`

Frictional force is given by

`f=-\mu mg\\\Rightarrow f=-(2)/(5)mg\\\Rightarrow ma_2=-(2)/(5)mg\\\Rightarrow a_2=-(2)/(5)g`

Net acceleration is given by

`a=a_2-a_1\\\Rightarrow a=-(2)/(5)g+(g)/(2)\\\Rightarrow a=(g)/(10)`

The acceleration of the box relative to the truck is
`(g)/(10)` and
`-(g)/(10)` relative to the road.