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.
A)0.42
B)0.54
C)0.17
D)0.33
E)This cannot be determined without knowing the mass of the box.

Question

Quizplus · Accepted Answer

The minimum coefficient of static friction can be found using the equation:
μs = (mv^2)/(rN)
where μs is the coefficient of static friction, m is the mass of the box, v is the speed of the car, r is the radius of the curve, and N is the normal force.
Since the box is stationary relative to the floor of the trunk, the maximum static friction force must be equal to the gravitational force acting on the box:
fstatic = μsN = mg
where g is the acceleration due to gravity.
We can rearrange this equation to solve for N:
N = m(g/μs)
Substitute this expression for N into the equation for μs:
μs = (mv^2)/(rg/μs)
Simplify and solve for μs:
μs^2 = (rg)/v^2
μs = √(rg)/v
μs = √(9.8 m/s^2 * 48 m)/(16 m/s) ≈ 0.54
Therefore, the minimum coefficient of static friction is 0.54.

Holly Puts a Box into the Trunk of Her Car