Question

You push horizontally on a 120-N box that is initially resting on a horizontal table. The coefficient of static friction between the box and the table is 0.75, and the coefficient of kinetic friction is 0.40. Find the friction force on the box if the push is equal to(a) 84 N; (b) 94 N.​

Answer 1

(a) When the applied force is 84 N, the friction force on the box is 36.02 N.

(b) When the applied force is 94 N, the friction force on the box is 46.02 N.

Frictional force on the box

The frictional force on the box when it is pushed with a certain force is calculated as follows;

Ff  = μFₙ

F - Ff = ma

Mass of the box is calculated as follows;

W = mg

m = W/g

m = 120/9.8

m = 12.24 kg

Acceleration of the box is calculated as follows;

a = μg

a = 0.4(9.8)

a = 3.92 m/s²

When the applied force is 84 N,

F - Ff = ma

F - ma = Ff

84 - 12.24(3.92) = Ff

36.02 N = Ff

When the applied force is 94 N,

F - Ff = ma

F - ma = Ff

94 - 12.24(3.92) = Ff

46.02 N = Ff

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