### Video Transcript

In the figure, the body is moving
at a constant velocity 𝑣 under the action of a system of forces. Given that the forces are measured
in newtons, find the magnitudes of 𝐹 and 𝑘.

We’re told that this body is moving
at a constant velocity under a number of forces. And so, we’re able to recall
Newton’s first law of motion. This says that if there’s no net
force, in other words, the forces acting on the body cancel each other out, the
object will maintain a constant velocity. So, for our body to maintain its
constant velocity under the action of the system of forces, we need the sum of these
forces to be equal to zero. Now, in fact, our forces are acting
in two dimensions. So, we could consider the
horizontal and vertical directions separately or think about it as a vector such
that the vector sum of the forces is equal to zero.

We’re going to think about this as
two directions, and we’re going to consider the vertical direction first. We’ll take upwards to be
positive. Now, it doesn’t really matter which
direction we choose to be positive as long as we’re consistent throughout the
question. The only force that we have acting
in that direction is force 𝐹. If we look carefully, we see that
the force that’s parallel to 𝐹 is 20, and that’s acting in the opposite
direction. So, the sum of these two forces
must be 𝐹 minus 20.

We also have a force of 31 newtons
acting in the negative direction. So, the sum of all of our forces
acting vertically is 𝐹 minus 20 minus 31. And of course, we know that this
must be equal to zero for our object to maintain a constant velocity. So let’s simplify the
expression. Negative 20 minus 31 becomes
negative 51. So, the sum of our forces is 𝐹
minus 51. And our equation is 𝐹 minus 51
equals zero. To solve this equation, to find the
value of 𝐹, we’re simply going to add 51 to both sides. And when we do, we find 𝐹 is equal
to 51. We were told that the forces are
measured in newtons. So, we can say 𝐹 must itself be 51
newtons.

We’re now going to repeat this
process in the horizontal direction. This time moving to the right is
our positive direction. The force given by the arrow acting
in this direction is 𝑘 newtons. Then, in the opposite direction, we
have 79 newtons. So, the sum of the forces acting on
this body in our horizontal direction is 𝑘 minus 79. Once again, we can set this equal
to zero because we’re told that the object has a constant velocity. Then, we solve for 𝑘. And we add 79 to both sides. And when we do, we find 𝑘 is equal
to 79 or 79 newtons. 𝐹 is, therefore, equal to 51
newtons and 𝑘 is equal to 79 newtons.