Video Transcript
An object that has a momentum of 12
kilogram-meters per second is acted on by a constant force for eight seconds, after
which the object’s momentum is six kilogram-meters per second. Determine the force that acted on
the object.
Okay, so we have an object that
starts out with a momentum of 12 kilogram-meters per second. Let’s imagine that this pink blob
here is our object. And we’ll label its initial
momentum as 𝐩 one so that we have 𝐩 one is equal to 12 kilogram-meters per
second. Now, momentum is a vector quantity,
which means that it has a direction as well as a magnitude. Let’s imagine that the object’s
momentum is in this direction. We are then told that the object is
acted on by a constant force for eight seconds and that after this eight-second
interval, the object’s momentum is six kilogram-meters per second. So we can draw our object again
after a time interval of eight seconds, which we’ve labeled as Δ𝑡. We’ll label its new momentum as 𝐩
two so that we have 𝐩 two is equal to six kilogram-meters per second.
Since the original momentum 𝐩 one
was positive and the new momentum 𝐩 two is also positive, then 𝐩 two will be in
the same direction as 𝐩 one. So we can represent that with an
arrow like this. We are asked to work out the force
which acted on the object to cause this change in momentum. We can recall that whenever we have
a force which acts to change the momentum of an object, then if the object’s
momentum changes by an amount of Δ𝐩 over a time interval of Δ𝑡, then the force 𝐹
which acts on that object is equal to Δ𝐩 divided by Δ𝑡. So we know the time interval Δ𝑡,
and we know the momentum the object started with and the momentum it ended up
with.
We can use these values of 𝐩 one
and 𝐩 two to calculate the change in the object’s momentum Δ𝐩. Δ𝐩 must be equal to the final
momentum 𝐩 two minus the initial momentum 𝐩 one. If we now sub in the values for 𝐩
two and 𝐩 one, we find that the change in momentum is equal to negative six
kilogram-meters per second. The value we’ve calculated for Δ𝐩
is negative because 𝐩 two is smaller than 𝐩 one. In other words, the momentum of the
object has decreased, and so we have a negative change in the object’s momentum. We now have values for both Δ𝐩 and
Δ𝑡. So it’s time to go ahead and sub
those values into this equation to calculate the force 𝐹. When we do this, we get that 𝐹 is
equal to negative six kilogram-meters per second divided by eight seconds.
At this stage, it’s worth pointing
out that the kilogram-meter per second is the SI base unit for momentum, and the
second is the SI base unit for time. So Δ𝐩 and Δ𝑡 are both expressed
in their SI base units. This means that the force 𝐹 that
we calculate will be in its own SI base unit, which is the newton. When we evaluate this expression
for 𝐹, we get a result of negative 0.75 newtons. The fact that this force is
negative means that it acts in the opposite direction to the object’s momentum. So since in our diagram we had the
momentum of the object directed to the right, then in this diagram, the force will
be directed to the left.
This force 𝐹 is exactly what we
were asked to calculate. And so our answer to the question
is that the force which acted on the object is equal to negative 0.75 newtons.
