Using static friction to find tension

In summary, the question asks for the minimum pulling force needed for a circus clown to yank his feet out from under himself. The clown weighs 860 N and the coefficient of static friction between his feet and the ground is 0.41. Using the F=ma equation, it can be calculated that the minimum pulling force needed is 507.4N. The friction is felt in the y-direction since the clown is standing on the floor. The normal force does play a role in this problem. To find the tension in the rope, the vertical force exerted by the rope on the clown, the normal force on the ground, and the horizontal force exerted by the rope on his feet, further information is needed.
  • #1
jenador
13
0
I am having a lot of problems with the tension/force questions on my homework. Here is the last question I don't understand in my homework set:

The drawing shows a circus clown who weighs 860 N. The coefficient of static friction between the clown's feet and the ground is 0.41. 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?

http://www.webassign.net/CJ/04_58.gif

I know that the clown is in equilibrium when he is not moving and if he yanks his feet off the floor. Using the F=ma equation, I figured he would move in the y-direction. therefore F=ma=-(his weight)+(friction)=-860N+(860*0.41)=507.4N.

Is that correct? Is it right to say that friction is felt in the y direction in this case because the clown is just standing on the floor? Does F(normal force) play a role in this problem?
 
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  • #2
If the clown pulls on the rope with a force F, what is the tension in the rope? What is the vertical force exerted by the rope on the clown? What is the normal force on the ground due to the clown? What is the horizontal force exerted by the rope on his feet?
 
  • #3


Yes, your approach is correct. The key concept here is that the clown is in equilibrium, meaning that the forces acting on him are balanced and he is not moving. This means that the force he exerts on the rope must be equal and opposite to the forces acting on him (his weight and the friction force).

To find the minimum pulling force, we need to consider the maximum possible friction force that can be exerted on the clown's feet. This is where the coefficient of friction comes into play. The coefficient of static friction is a measure of how much force is needed to overcome the friction between two surfaces. In this case, the coefficient of static friction between the clown's feet and the ground is 0.41, meaning that the maximum friction force that can be exerted on the clown's feet is 0.41 times his weight, or 0.41*860 N = 353.6 N.

So to find the minimum pulling force, we need to add the maximum friction force to the clown's weight, giving us a total of 860 N + 353.6 N = 1213.6 N. This is the minimum force that the clown must exert on the rope to yank his feet out from under himself.

In terms of the direction of the friction force, it is indeed acting in the y-direction (vertical) in this case because the clown is standing on the ground and the rope is pulling downwards. And yes, the normal force (the force exerted by the ground on the clown's feet) does play a role in this problem as it is what enables the friction force to act on the clown's feet.

I hope this explanation helps you better understand the concept of using static friction to find tension in a situation like this. Keep practicing and don't hesitate to ask for clarification if needed. Good luck with your homework!
 

1. How do you use static friction to find tension?

To use static friction to find tension, you need to set up an experiment where an object is suspended by a rope or cable. The weight of the object creates a downward force, while the rope provides an upward force to counteract it. By slowly increasing the weight of the object until it starts to move, you can measure the maximum static friction force. This force is equal to the tension in the rope.

2. What is static friction?

Static friction is a type of friction that occurs when two surfaces are in contact with each other, but not moving relative to one another. It is a force that acts in the opposite direction of any applied force, preventing the objects from moving.

3. How does static friction differ from kinetic friction?

Static friction occurs when two objects are not moving relative to each other, while kinetic friction occurs when two objects are in motion. Static friction is typically greater than kinetic friction, as it takes more force to overcome the initial resistance between two stationary objects.

4. Why is static friction important in finding tension?

Static friction is important in finding tension because it is the force that allows an object to remain stationary when an opposing force is applied. In the case of an object suspended by a rope, the maximum static friction force is equal to the tension in the rope.

5. Are there any limitations to using static friction to find tension?

While using static friction to find tension can be a useful tool, there are some limitations to keep in mind. For example, the surface roughness and material properties of the objects in contact can affect the accuracy of the measurements. Additionally, if the applied force is too great, the objects may start to slide instead of experiencing static friction, making it difficult to determine the maximum static friction force.

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