In the previous section on dragging blocks,
we considered only an example without friction.
In this section, on blocks with kinetic friction,
we will add a fourth force to our freebody diagram.
Important Rule
To do the problems in this section, you will need to use Newton's Second Law:
$$
\Sigma F = ma
$$
Forces 1  3:

Gravity

The direction of gravity is always downward.

The magnitude of gravity
is given by the formula \( F_g = mg \).

Normal Force

The direction of the normal force
is always perpendicular to the surface,
which in this case is upward.

The magnitude of the normal force
is a very difficult concept. For these problems,
the magnitude of the normal force is equal to the
magnitude of gravity.
(In the elevator problems, it is not!)

Applied Force

The direction of the applied force
is typically given in the problem.

The magnitude of the applied force
is also typically given int he problem.
Force 4: Kinetic Friction
Kinetic friction is a force that acts on anything that is sliding on a surface.
It is the force that makes moving things difficult.

The magnitude of kinetic friction
is given by the formula \( F_{frk} = \mu_k F_N \).

The direction of kinetic friction is always
in the direction opposite the direction
the box is moving.
$$
F_{frk} = \mu_k F_N
$$
The value \( \mu_k \) is called the coefficient of kinetic friction.
It is property of the two objects being rubbed together.
A greater coefficient of kinetic friction indicates that the objects have rougher
surfaces and thus more friction.
It is usually a value less than 0.5.
It is frequently given in the problem, or the goal of the problem is to discover it.
Finding Acceleration:

A 2.00 kg block is being dragged on a surface with friction
by an applied force of 44.0 Newtons to the right.
It is accelerating because of the pull!
The coefficient of kinetic friction between the block and the surface is 0.400.

Use the information to fill out the table below:

The two vertical forces cancel out in this problem,
but there are two different horizontal forces.
Determine the net force (magnitude and direction) acting on the block.

Determine the magnitude of acceleration \( a\) of the block.

A 8.00 kg block is being dragged on a surface with friction
by an applied force of 48.0 Newtons to the RIGHT.
It is accelerating because of the pull!
The coefficient of kinetic friction between the block and the surface is 0.380.

Use the information to fill out the table below:

The two vertical forces cancel out in this problem,
but there are two different horizontal forces.
Determine the net force (magnitude and direction) acting on the block.

Determine the magnitude of acceleration \( a \) of the block.
Finding \( \mu_k \)
In these problems, you will need to use the principles
above, along with Newton's First Law,
to determine the coefficient of kinetic friction.
Newtons First Law:
If an object is either not moving or moving at a constant velocity,
the net force acting on that object is zero.

A 2.00 kg block is being dragged to the right on a surface at a constant velocity
by a force of 16.0 Newtons.

What is the net force acting on this block?
How do you know? Refer explicitly to one of the laws of physics in your answer.

Fill out the table below to analyze the forces acting on the box.
You won't be able to fill it out the same order you did problems 1 and 2.
You will need to think about it a little differently.

Determine the coefficient of kinetic friction \( \mu_k \)
between the block and the surface.

A 12.0 kg block is being dragged to the right on a surface at a constant velocity
by a force of 44.0 Newtons.

What is the net force acting on this block?
How do you know? Refer explicitly to one of the laws of physics in your answer.

Fill out the table below to analyze the forces acting on the box.

Determine the coefficient of kinetic friction \( \mu_k \)
between the block and the surface.
Extra Problems
(It is not necessary to complete these problems when turning in the practice page.)

A 6.00 kg block is being dragged on a surface with friction
by an applied force of 18.0 Newtons to the RIGHT.
It is accelerating because of the pull!
The coefficient of kinetic friction between the block and the surface is 0.220.

Use the information to fill out the table below:

The two vertical forces cancel out in this problem,
but there are two different horizontal forces.
Determine the net force (magnitude and direction) acting on the block.

Determine the magnitude of acceleration \( a \) of the block.

A 0.500 kg block is being dragged to the right on a surface at a constant velocity
by a force of 1.20 Newtons.

What is the net force acting on this block?
How do you know? Refer explicitly to one of the laws of physics in your answer.

Fill out the table below to analyze the forces acting on the box.

Determine the coefficient of kinetic friction \( \mu_k \)
between the block and the surface.