A 2.0-kg silverware drawer does not slide readily. The owner gradually pulls with more and more force, and when the applied force reaches 9.0 N, the drawer suddenly opens, throwing all the utensils to the floor. What is the coefficient of static friction between the drawer and the cabinet?

For static body, the frictional force (Ff) acting on the body is equal to the moving force (Fm) since both forces acts along the horizontal on the body.

Ff = Fm = 9.0N

The normal reaction (R) on the body will also be equal to its weight(W) since weight acts downwards and the reaction acts in the opposite direction (upwards).

R = W = 20N

Ff = nR taking 'n' as coefficient of static friction between the drawer and the cabinet.

9.0 = 20n

n = 9/20

n = 0.45

dsdrajlin dsdrajlin · Answer 2 · 2021-10-29T15:55:50+02:00

A 2.0-kg silverware drawer opens suddenly when the applied force reaches 9.0 N. The coefficient of static friction between the drawer and the cabinet is 0.46.

A drawer starts moving when the force applied is 9.0 N. At that moment, the force done by the person and the force of static friction are balanced. Thus the force of static friction (F) is 9.0 N.

We can calculate the coefficient of static friction (k) using the following expression.

[tex]F = k \times N = k \times m \times g[/tex]

where,

N: normal force

m: mass of the drawer

g: gravity (9.8 m/s²)

The coefficient of static friction is:

[tex]k = \frac{F}{m \times g } = \frac{9.0N}{2.0kg \times (9.8m/s^{2} ) } = 0.46[/tex]

A 2.0-kg silverware drawer opens suddenly when the applied force reaches 9.0 N. The coefficient of static friction between the drawer and the cabinet is 0.46.

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