A 55.0 kg box is placed on an inclined plane that makes an angle of 28.0 degrees with the horizontal. The coefficient of static friction between the box and the inclined plane is 0.680. Determine the static frictional force which holds the box in place.

253 N

Explanation:

The forces acting on the box in the direction along the ramp are two:

- The component of the weight in the direction parallel to the ramp, , acting down along the ramp

- The force of static friction, , acting up along the ramp

The equation of motion along this direction is:

where:

m = 55.0 kg is the mass of the box

is the acceleration of gravity

is the angle at the base of the ramp

a is the acceleration of the box

However in this proble, the box is at rest, so the acceleration is zero:

Therefore, the equation becomes:

From which we find the static frictional force:

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