Video Transcript
A cup of mass 125 grams is at rest
on a desk when it is accidentally knocked by a person’s arm. The cup accelerates in the
direction that it is pushed at a rate of 0.25 meters per second squared. How much force is applied by the
arm that knocks the cup? Give your answer to two decimal
places.
Okay, so in this question, we know
that we’ve got a cup which has a mass of 125 grams, and initially it’s at rest on a
desk. We know that this cup is then
knocked by a person’s arm, applying some force to it, which causes it to accelerate
in the direction it is pushed. We’re told that the acceleration
has a magnitude of 0.25 meters per second squared. We need to work out the amount of
force, which we’ve labeled 𝐅, applied by the arm which knocks the cup.
To solve this question, we’ll need
to find a relationship between the acceleration of the cup, 𝑎, the force exerted on
the cup, 𝐅, and the cup’s mass, 𝑚. This relationship is Newton’s
second law of motion, which says that the force 𝐅 applied to an object is equal to
the object’s mass, 𝑚, multiplied by the acceleration, 𝑎, that the object
experiences. Since in this case we know the
values of 𝑚 and 𝑎, we can use this equation from Newton’s second law in order to
work out the force applied to the cup. Before we do this, though, we need
to consider the units of the quantities.
If we want to find the force in
newtons, which is the standard SI unit of force, then we need to have the mass and
the acceleration in their standard units as well. The standard unit of mass is the
kilogram, and the standard unit of acceleration is meters per second squared. Our value for the acceleration, 𝑎,
of the cup already has units of meters per second squared. However, the mass, 𝑚, is in units
of grams rather than kilograms. We therefore need to convert this
value from grams into kilograms. Let’s recall that one kilogram is
equal to 1000 grams. Dividing both sides of this
equation by 1000, we see that one gram is equal to one thousandth of a kilogram. So to convert this mass 𝑚 from
grams into kilograms, we need to multiply it by one over 1000 kilograms per
gram. We find then that the mass of the
cup is 0.125 kilograms.
We are now ready to take our values
for the mass, 𝑚, and acceleration, 𝑎, and substitute them into this equation for
the force, 𝐅. We have that 𝐅 is equal to 0.125
kilograms multiplied by 0.25 meters per second squared. Evaluating this gives a force of
0.03125 newtons. Notice though that we’re asked to
give our answer to two decimal places. To two decimal places, our result
rounds down to 0.03 newtons.
Our final answer then is that the
force applied by the arm that knocks the cup is 0.03 newtons.
