A 2.0 kg block rests on a level surface. The coefficient of static friction is, and the coefficient of kinetic friction is A horizontal force, X, is applied to the block. As X is increased, the block begins moving. Describe how the force of friction varies as X increases from the moment the block is at rest to when it begins moving. Indicate how you could determine the force of friction at each value of X―before the block starts moving, at the point it starts moving, and after it is moving. Show your work. ps. I had to change F to X because of .

By Newton's second law, the net force acting on the block in the vertical direction is

∑ F [ver] = n - mg = 0

where n = magnitude of normal force and mg = weight of the block. It follows that n = mg.

When the block is at rest, the applied force X will not be enough to move the box until it can overcome the maximum mag. of static friction. If µ[s] is the coefficient of static friction, then the maximum mag. of the frictional force is

f = µ[s] n = µ[s] mg

The net horizontal force would be

∑ F [hor] = X - µ[s] mg = 0

so a minimum force of X = µ[s] mg is required to get the block moving. Any mag. smaller than this and the block stays at rest/in equilibrium.

Once the mag. of X exceeds µ[s] mg, the block will begin to move. At that point, if the coefficient of kinetic friction is µ[k], then the net force on the block is

∑ F [hor] = X - µ[k] mg = 0

so a minimum force of X = µ[k] mg would be needed to keep the block moving at constant speed, or otherwise X = µ[k] mg + ma if the block is accelerating with mag. a.

The principles here are captured in the attached plot.

your answer is yx

hope this

~mia

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