The drawing shows a circus clown who weighs 710 N. The coefficient of static friction between the clown's feet and the ground is 0.49. 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?
y: mg=T+N
x: F(fr)=T
N=mg-T
F(fr)= μN=μ(mg- T) = μmg-μT =T
T(1+μ)= μmg
T= μmg/(1+μ)=0.49•710/1.49=233.5 Newtons
To determine the minimum pulling force that the clown must exert to yank his feet out from under himself, we need to analyze the forces acting on the clown.
Let's break down the problem step-by-step:
Step 1: Identify the forces acting on the clown:
- Weight of the clown (acting downward) = 710 N
- Normal force (acting upward) = equal in magnitude and opposite in direction to the weight of the clown
- Frictional force (acting horizontally) = opposing the motion
Step 2: Calculate the normal force:
The normal force is equal in magnitude and opposite in direction to the weight of the clown, which is 710 N.
Step 3: Calculate the maximum frictional force:
The maximum frictional force can be determined using the formula: maximum frictional force = coefficient of static friction * normal force.
Given that the coefficient of static friction is 0.49 and the normal force is 710 N, the maximum frictional force is: maximum frictional force = 0.49 * 710 = 347.9 N.
Step 4: Calculate the minimum pulling force:
To yank his feet out from under himself, the clown needs to overcome the maximum frictional force. Therefore, the minimum pulling force equals the maximum frictional force.
Thus, the minimum pulling force required is 347.9 N.
To find the minimum pulling force that the clown must exert to yank his feet out from under himself, we need to analyze the forces acting on the clown.
1. Identify the forces:
- The weight of the clown (W) = 710 N, acting vertically downward.
- The normal force (N) exerted by the ground on the clown, equal in magnitude and opposite in direction to the weight of the clown.
2. Determine the maximum static friction force:
The maximum static friction force (f_s) that can be exerted between two surfaces is given by the formula: f_s = μ * N, where μ is the coefficient of static friction and N is the normal force.
In this case, the coefficient of static friction is given as 0.49. Therefore, the maximum static friction force is: f_s = 0.49 * N.
3. Analyze the forces acting on the clown:
To yank his feet out from under himself, the clown must exert a force greater than the maximum static friction force. The maximum static friction force opposes the pulling force and keeps the clown's feet in place. Once the pulling force exceeds this maximum static friction force, the clown's feet will be free to move.
4. Calculate the minimum pulling force:
To find the minimum pulling force, we equate the maximum static friction force to the pulling force.
Therefore, 0.49 * N = F, where F is the minimum pulling force.
However, we need to find the value of N to solve this equation.
Using Newton's second law in the vertical direction, we know that:
Net force in the vertical direction = Weight of the clown - Normal force
So, the equation becomes: N = W
Substituting this value of N into the equation 0.49 * N = F, we now have:
0.49 * W = F
Substituting the known value of W (710 N) into the equation, we can calculate the minimum pulling force:
0.49 * 710 N = F
F ≈ 348.9 N
Therefore, the clown must exert a minimum pulling force of approximately 348.9 N to yank his feet out from under himself.