# Several students visit a playground and one of them pushes the others on a merry-go-round.The diameter of the merry-go-round is 3.0 m, and the student pushes with a force of 50 N. a) What torque...

Several students visit a playground and one of them pushes the others on a merry-go-round.

The diameter of the merry-go-round is 3.0 m, and the student pushes with a force of 50 N.

a) What torque does the student apply?

b) What angle would the student need to apply the force at, to achieve maximum torque?

c) If the student continues to push with a force of 50 N, what maximum torque could be applied?

The present angle between the force and the radius vector is 110 degrees.

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### 2 Answers

The torque applied by the student is given as T = F * r * sin A, where F is the force, r is the radius vector and A is the angle between the radius vector and the force vector.

- The torque applied by the student is 50*3* sin 110

=> 140.95 N.m

- To achieve maximum torque the student would have to apply the force in a direction that forms an angle of 90 degrees with the direction of the radius vector.

- If the force applied by the student is 50 N, he can increase the torque to a maximum of 50*3*sin 90 = 150 N.m by changing the direction at which the torque is being applied.

for a) wouldnt the radius (half the diameter) actually be 1.5?

so it's 50*1.5*sin110 = 70.48 n.m