PhysicsBowl 2017 Q26

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PhysicsBowl 2017

26) For this question, we have a being swung in circular motion, shown in the diagram provided. Our goal is to find the speed of this mass. As with any dynamics problem, we should start with a free-body diagram. To make the problem simpler, we will split the forces into their x and y components.

Where T is tension, and F[g] is gravitational force

By using the components, we can set up a system of equations. The object doesn't move up or down in the y-plane, so the net acceleration of the y-components is 0. Additionally, we also know that the object is in circular motion produced by the forces in the x-direction, so we can equate this to the centripetal force.

Where F is force, T is tension, F[c] is centripetal force, θ is measure of angle, m is mass, v is speed, r is radius, F[g] is gravitational force, and g is acceleration due to gravity

By dividing equations 1 and 2, we can solve for a combined equation for the speed.

Where T is tension, θ is measure of angle, m is mass, v is speed, r is radius, F[g] is gravitational force, and g is acceleration due to gravity

Next, we need to find out the value of the radius r.

Where r is radius, and L is length of string

Finally, plugging all of this into our equation, we can solve for the speed.

Where v is velocity, r is radius, g is acceleration due to gravity, θ is the measure of the angle, and L is length of the string

Answer: A