When an object is on an incline, the incline exerts a force on the object. We ca

Question

When an object is on an incline, the incline exerts a force on the object. We call the perpendicular component the “normal force” (where normal is a mathematical term meaning perpendicular) and we call the parallel component the “friction force”. What happens to the magnitude of the normal force on an object as the angle of the incline is increased?

It can be shown that when the object does not slip down the incline, the ratio of the friction force acting parallel to the incline and the normal force acting perpendicular to the incline is equal to the ratio of the height of the ramp to its horizontal distance. This is the definition of the tangent of the angle. We call the coefficient of static friction (s) the maximum value this ratio can be before slipping. Use a scientific calculator to verify that if the block begins slipping for angles above 30 degrees that s = tan(30) = 0.577.

A person applied a horizontal force of 75 N to a crate that caused the crate to move at a constant velocity. What is the magnitude of the net force on the crate? What is the magnitude of the friction force on the crate?

Explanation / Answer

formula for normal force is

N = mg cos theta

when theta increases normal force decreases.

Apply Newton second law to the crate

F- fk = ma

since crate moving with constant velocity so a= 0

F-fk = 0

F = fk

= uk mg cos theta

= 0.577 ( 75) cos 30

=37.47 N

net force and frction force is same becuase crate moving with constant velocity

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