### Video Transcript

A bus is moving at a speed of 16
meters per second on a uniform circular path that has a radius of 150 meters. If the centripetal force needed to
keep the bus on the circular path is 2.3 times 10 to the power of three newtons,
what is the mass of the bus? (A) 1347.66 kilograms, (B) 2156.25
kilograms, (C) 3925.33 kilograms, (D) 21562.5 kilograms.

Here we are being asked to consider
the centripetal force required to keep a bus moving along a circular path. If we know this force, as well as
the radius of the circle and the speed at which the bus moves, then we can recall
the equation that relates these quantities with the mass of the bus.

The centripetal force acting on an
object is given by the following equation. πΉ equals ππ£ squared over π,
where π is the mass of the object, π£ is its speed as it moves along the circle,
and π is the radius of the circle.

Since weβve been asked to solve for
the mass of the bus, letβs rearrange this equation. We can multiply both sides of the
equation by π over π£ squared. This way, the π£ squared over π
cancels on the right-hand side. And weβre left with π equals πΉπ
over π£ squared.

Next, we can check that all the
quantities given to us in the question are in their standard SI units. The speed of the bus is 16 meters
per second. The radius of the circle is 150
meters. And the centripetal force is 2.3
times 10 to the power of three newtons. These are all in the correct
units. So we can substitute them into the
right-hand side of our equation.

And we see that the mass is equal
to 2.3 times 10 to the power of three newtons multiplied by 150 meters over 16
meters per second squared. We therefore find the mass of the
bus to be 1347.65625 kilograms. Rounding this to two decimal
places, we see that this matches our answer option (A). Hence, the mass of the bus is
1347.66 kilograms.