### Video Transcript

In the given figure, the body is
moving with uniform velocity under the action of a system of forces. Given that the forces are measured
in newtons, find the magnitudes of 𝐹 and 𝐾.

The key piece of information that
will help us solve this question is that we are told the body is moving with uniform
velocity. This means that the body will not
be accelerating. And using standard units, we can
say that the acceleration is equal to zero meters per second squared. Newton′s first law tells us that an
object remains in the same state of motion unless a resultant force acts on it.

This means that if the resultant
force on an object is zero, a stationary object stays stationary and a moving object
continues to move at the same velocity. This is the case in this question,
which means that the sum of the forces in the horizontal direction must be zero and
in the same way the sum of the forces in the vertical direction must be zero.

Let′s begin by considering the
forces acting in a vertical direction. We have the 57-newton force
together with a force 𝐹. If we let the positive direction be
vertically upwards, the sum of our forces is 57 minus 𝐹. And we know this must be equal to
zero. Adding 𝐹 to both sides, we have 𝐹
is equal to 57. Since our forces are measured in
newtons, we have 𝐹 is equal to 57 newtons. Next, we consider the forces acting
horizontally. And we will take the positive
direction to be to the right.

We have positive forces equal to 66
and 27 newtons and a negative force of 𝐾. Setting this equal to zero gives us
66 plus 27 minus 𝐾 equals zero. This time, adding 𝐾 to both sides
of our equation, we have 𝐾 is equal to 93. If the body in the figure is moving
with uniform velocity, then 𝐹 is equal to 57 newtons and 𝐾 is equal to 93
newtons.