Question Video: Calculating the Mass of a Bus in Uniform Circular Motion | Nagwa Question Video: Calculating the Mass of a Bus in Uniform Circular Motion | Nagwa

Question Video: Calculating the Mass of a Bus in Uniform Circular Motion Physics • First Year of Secondary School

A bus is moving at a speed of 16 m/s on a uniform circular path that has a radius of 150 m. If the centripetal force needed to keep the bus on the circular path is 2.3 Γ— 10Β³ N, what is the mass of the bus?

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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. 𝐹 equals π‘šπ‘£ squared over π‘Ÿ, where π‘š is the mass of the object, 𝑣 is its speed as it moves along the circle, and π‘Ÿ is the radius of the circle.

Since we’ve been asked to solve for the mass of the bus, let’s rearrange this equation. We can multiply both sides of the equation by π‘Ÿ over 𝑣 squared. This way, the 𝑣 squared over π‘Ÿ cancels on the right-hand side. And we’re left with π‘š equals πΉπ‘Ÿ over 𝑣 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.

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