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3 years ago

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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 t

he 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.

1 answer:

LiRa [457]3 years ago

3 0

Answer:

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:

$F_{c} = \frac{mv^{2}}{R}$

$f_{s} = \mu_{s}mg$

where

$\mu_{s}$ = coefficient of static friction

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

$F_{net} = f_{s} - F_{c}$

$0 = f_{s} - F_{c}$

$\mu_{s}mg = \frac{mv^{2}}{R}$

$\mu_{s} = \frac{v^{2}}{gR}$

$\mu_{s} = \frac{16^{2}}{9.8\times 48} = 0.544$

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