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Minimum Pulling Force Sample Assignment

Question: A circus clown weighs 900 N. The coefficient of static friction between the clown's feet and the ground is 0.4. He pulls vertically downward on a rope that passes around three pulleys and is tied around his feet. What is the minimum pulling force that the clown must exert to yank his feet out from under himself?

Ans:  There are the following forces acting on the clown:

Tension force (applied to the hand) – direction upward

Gravitational force – direction downward,

Normal force – direction upward;

Friction force – direction horizontal;

Tension force (applied to clown's legs) – direction horizontal.

Then the minimum tension force correspond to the condition that the friction force is equal to 0.4*normal force.

In terms of x (horizontal) and y (vertical) components we have:

                                           T + n = mg

                                                  f_s = T

Then,                                        n = mg - T = 900 - T

                                                  f_s = 0.4n = 0.4 * (900 - T) = T

                                                 0.4 * 900 = 1.4T

                                                              T = 257 N

Other Sample Assignments in Physics Homework Assignment :

Work Energy Power	Minimum Pulling Force
Shear Stress	Loss in Kinetic Energy
Impulse

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