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A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 1000N, the players have equal pulls, and the angle between the two ropes is 20. How hard must each player pull to drag the coach at a steady2.0m/s?

Short Answer

Expert verified

Each player requires the force of 508Nto pull the rope.

Step by step solution

01

Force :

The force exerted on a mass that causes it to change velocity.

02

Explanation :

1000Nis the friction force on the sled. 20is the angle between the two ropes and the players drag the sled with equal force at a steady speed of 2.0m/s.

The free body diagram of the arrangement is shown:

Using Newton's second law, Fx=ma

where, mass of the player is mand acceleration of the player is a.

But, here the players drag the sled with constant steady speed of 2.0m/s. So, the acceleration is zero as the rate of change of velocity is zero.

Substitute 0m/s2for a.

Fx=m0m/s2Fx=0

Resolving the components of forces in the ropes in x-direction,

-Ff+2Tcos=0

The tension in the rope or the force at which the each player pull the rope is T.

The angle made by the rope with the sled is .

The friction force is Ff.

Substitute 1000Nfor Ffand 10for .

-1000N+2Tcos10=0T=1000N2cos10=507.71508N

Hence, force required by each player to pull the rope is508N.

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