### Video Transcript

A body weighing 25.5 newtons rests
on a rough horizontal plane. A horizontal force acts on the
body, causing it to be on the point of moving. Given that the coefficient of
friction between the body and the plane is three seventeenths, determine the
magnitude of the force.

We can begin by sketching a diagram
to model the situation. We know that any body resting on a
horizontal plane will have a downward force equal to its weight. And this weight π will be equal to
the mass of the body multiplied by the acceleration due to gravity. In this question, we are told the
body weighs 25.5 newtons. So there will be a force acting
vertically downwards equal to 25.5 newtons. Newtonβs third law tells us that
there will be a normal reaction force acting in the opposite direction to this. Since the body is in equilibrium,
we know that these two forces are equal. The normal reaction force π is
equal to 25.5 newtons.

We are told that a horizontal force
π
acts on the body. And as the plane is rough, there
will be a frictional force acting between the body and the plane. The body is on the point of moving,
which means that the frictional force will be at its maximum. This is known as the limiting
friction such that π
π is equal to π multiplied by π, where π is the coefficient
of friction between the body and the plane. In this question, we are told this
is equal to three seventeenths. The frictional force π
π is
therefore equal to three seventeenths multiplied by 25.5, which is equal to 4.5. The maximum frictional force is
equal to 4.5 newtons.

Since the body is on the point of
moving and is still in equilibrium, the horizontal forces must also be equal to one
another. The applied force π
must be equal
to the frictional force π
π. We can therefore conclude that the
magnitude of the horizontal force acting on the body is 4.5 newtons.