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A 4.6 kg block is at rest on a 32° plane. The coefficient of static friction is 0.8. What is the static frictional force on the block?

A. 23.9 N
B. 30.6 N
C. 38.2 N
D. 45.1 N

Answer :

Final answer:

The static frictional force on the block can be calculated by first determining the block's weight perpendicular to the inclined plane and then multiplying this value by the coefficient of static friction. The result is approximately 30.6 N.

Explanation:

To calculate the static frictional force on the block, we need to first consider the weight of the block perpendicular to the inclined plane. This is calculated as w = mass x gravity x cos(θ), where θ is the angle of the plane, gravity is approximately 9.8 m/s², and the mass is 4.6 kg. So, w = 4.6 kg * 9.8 m/s² * cos(32°) = 38.36 N approximately.

Next, using this value, we calculate the maximum force of static friction, which is the coefficient of static friction multiplied by the normal force (the weight we just calculated). Therefore, the static frictional force f = μs x N, where μs is the coefficient of static friction, and N is the normal force (w in our case). Substituting the values, f = 0.8 * 38.36 N = 30.69 N approximately. The closest answer to this is (b) 30.6 N.

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