The drawing shows a circus clown who weighs 750 N. The coefficient of static friction between the clown’s feet and the ground is 0.630. 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?
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To determine the minimum pulling force required for the clown to yank his feet out from under himself, we need to analyze the forces acting on the clown and use the concept of static friction.
First, let's consider the forces acting on the clown. We have the weight of the clown pulling downward, which we'll denote as F_weight. In this case, the weight of the clown is given as 750 N.
Now, let's analyze the forces due to static friction. Static friction acts between two surfaces in contact and prevents relative motion between them. The maximum static friction force (F_static_friction) can be calculated using the coefficient of static friction (μ) and the normal force (F_normal). In this case, the normal force is equal to the weight of the clown since the clown is standing on the ground.
F_static_friction = μ * F_normal
Since F_normal is equal to F_weight, we can substitute it into the equation:
F_static_friction = μ * F_weight
Given that the coefficient of static friction (μ) is 0.630 and the weight of the clown (F_weight) is 750 N, we can calculate the maximum force of static friction:
F_static_friction = 0.630 * 750 N
F_static_friction = 472.5 N
The maximum force of static friction (F_static_friction) represents the maximum force that can be exerted horizontally without causing the clown's feet to slide.
To yank his feet out from under himself, the minimum pulling force exerted by the clown must exceed the maximum static friction force. Therefore, the minimum force required is the force of static friction plus the weight of the clown:
Minimum pulling force = F_static_friction + F_weight
Minimum pulling force = 472.5 N + 750 N
Minimum pulling force = 1222.5 N
Hence, the minimum pulling force that the clown must exert to yank his feet out from under himself is 1222.5 N.