The equation for the force of friction is , where  is the coefficient of static friction.

The normal force is equal to the mass times acceleration due to gravity, but in the opposite direction (negative of the force of gravity).

Since the problem tells us that the force due to friction is , we can plug these values into our original equation to solve for the coefficient of friction.

The coefficient of friction has no units.

The equation for the force of friction is , where  is the coefficient of static friction.

The normal force is equal to the mass times acceleration due to gravity, but in the opposite direction (negative the force of gravity).

Since the problem tells us that the coefficient due to friction is equal to , we can plug these values into our original equation to solve for the force.

As the force due to friction is moving in the OPPOSITE direction to the force Mary will exert, it should appropriately be labelled as negative.

The equation for the force due to friction is , where  is the coefficient of kinetic friction. Since there is only one force acting upon the object, the force due to friction, we can find its value using the equation . We can equate these two force equations, meaning that . We can solve for the normal force, but we need to find  in order to find .

The problem gives us the mass of the crate, but we have to solve for the acceleration.

Start by finding the initial velocity. The problem gives us distance, final velocity, and change in time. We can use these values in the equation below to solve for the initial velocity.

Plug in our given values and solve.

We can use a linear motion equation to solve for the acceleration, using the velocity we just found. We now have the distance, time, and initial velocity.

Plug in the given values to solve for acceleration.

Now that we have the acceleration and the mass, we can return to our first equation for force.

The normal force is the same as the mass times gravity.

In this format, the masses cancel on both sides of the equation/

Now we can plug in our value for acceleration and gravity to solve for the coefficient of friction.

The problem gives us the minimum force required to move the cabinet. That means the force Erin exerts will be equal to the force due to friction, but moving in the opposite direction. 

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From here, expand the right side using the formula for kinetic friction and normal force.

Use the given values for the force, mass, and acceleration of gravity to solve for the coefficient of friction.

The force due to friction on a level surface is the product of the normal force and the coefficient of friction:

We are told the force required to move the block, which will be equal to the force of friction, and the mass of the block. Use the mass of the block to calculate the normal force.

Use the normal force and the force of friction to solve for the coefficient of friction.

Kinetic friction is never greater than static friction. More force is always requires to overcome static friction than is required to overcome kinetic friction. It can require a large force to initiate motion, causing an initial acceleration by overcoming static friction. Once motion has begun, however, less for is required to maintain the motion due to the principles of Newton's first law and inertia.