A 20.0 kg block is being pushed forward on a flat surface with a force of magnitude 45.0 N against a frictional force of 13.0 N

To draw this free-body diagram, would I only have the forces mentioned in the question? or would i include the -9.8m/s^2 force of gravity? Also, how would I find the change in kinetic energy if the block is pushed 4 m?

You only need the horizontal forces in this case because the friction force(not the coefficient) is given.

45 - 13 = 20 a

work done = change in kinetic energy
= (45 - 13) (4) Newton meters or Joules

To draw the free-body diagram for the 20.0 kg block, you need to include all the forces acting on it. The forces mentioned in the question are the force applied forward (45.0 N) and the frictional force opposing the motion (13.0 N). Additionally, you would include the force of gravity, which acts downward with a magnitude of (20.0 kg) * (9.8 m/s^2) = 196.0 N.

So, the free-body diagram for the block would include the following forces:

1. Force applied forward (45.0 N): Draw an arrow pointing to the right, labeled "45.0 N".
2. Frictional force opposing motion (13.0 N): Draw an arrow pointing to the left, labeled "13.0 N".
3. Force of gravity (196.0 N): Draw an arrow pointing downward, labeled "196.0 N".

To find the change in kinetic energy when the block is pushed 4 m, you need to calculate the work done on the block.

The work done on an object is given by the formula:

Work = Force * Distance * cos(theta)

In this case, the force applied (45.0 N) is in the same direction as the displacement (4 m), so the angle theta between them is 0 degrees and cos(theta) = 1.

Therefore, the work done on the block is:

Work = (45.0 N) * (4 m) * cos(0) = 180.0 N·m = 180.0 J (Joules).

The change in kinetic energy is equal to the work done on the block. So, the change in kinetic energy is 180.0 Joules.

To draw the free-body diagram, you would need to include all the forces acting on the block. In this case, you should include the force of gravity as well as the force being applied and the frictional force.

The force of gravity can be calculated using the mass of the block (20.0 kg) and the acceleration due to gravity (9.8 m/s^2). The force of gravity is given by:

Force_gravity = mass * acceleration due to gravity
= 20.0 kg * 9.8 m/s^2
= 196.0 N

So, you should include this force in your free-body diagram.

To find the change in kinetic energy if the block is pushed 4 m, you can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy. The work done is given by:

Work = force * distance

In this case, the force applied is 45.0 N, and the distance is 4 m. So, the work done is:

Work = 45.0 N * 4 m
= 180.0 J (joules)

Since work is equal to the change in kinetic energy, the change in kinetic energy is also 180.0 J.