Question

Holly puts a box into the trunk of her car. Later, she drives around an unbanked curve that has a radius of 48 m. The speed of the car on the curve is 16 m/s, but the box remains stationary relative to the floor of the trunk. Determine the minimum coefficient of static friction for the box on the floor of the trunk.

Answer 1

The minimum coefficient of friction is 0.544

Solution:

As per the question:

Radius of the curve, R = 48 m

Speed of the car, v = 16 m/s

To calculate the minimum coefficient of static friction:

The centrifugal force on the box is in the outward direction and is given by:

`F_(c) = (mv^(2))/(R)`

`f_(s) = \mu_(s)mg`

where

`\mu_(s)` = coefficient of static friction

The net force on the box is zero, since, the box is stationary and is given by:

`F_(net) = f_(s) - F_(c)`

`0 = f_(s) - F_(c)`

`\mu_(s)mg = (mv^(2))/(R)`

`\mu_(s) = (v^(2))/(gR)`

`\mu_(s) = (16^(2))/(9.8* 48) = 0.544`