Calculate the normal force and the tension in the string

In summary: So, I guess the problem is with the back of the book. Thanks for the help.In summary, the problem is that the answer for the tension in a string attached to an inclined plane is not 508 N, as the book says it should be. The answer is actually 425 N and 245 N.
  • #1
hadoken22
5
0
Hello. I am starting tension in my physics class and am stuck on a problem. I was wondering if anyone could help me out. It seems really simple: an object of mass 50kg is being held by a string attached to the top of a frictionless inclined plane that is 60 degrees above the horizontal. I need to calculate the normal force and the tension in the string.
I am really not sure how to solve this problem. My thinking was that the normal force exerted by the inclined plane would be equal in magnitude to the force of gravity, but opposite in direction. Fg=50kg*9.81*sin(60)=-Fn But, I am not sure that this is really true. It could be that the force of gravity is equal to the sum of the tension and the normal force. I tried breaking the forces down to their components and summing them up, but I did not get very far. I feel that I am failing to grasp some fundamental concepts. Any help would be greatly appreciated. Also, the answer is supposed to be 508 Newtons.
Thank you!
 
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  • #2
I tried breaking the forces down to their components and summing them up, but I did not get very far
Well, that is the way to solve this problem, so why did you not get very far? How did you go about doing this?

Also, what answer is supposed to be 508 N? Are you sure about that? You said you are to calculate the tension and the normal force. Neither of those is going to be 508N, assuming the string is parallel to the surface of the inclined plane. Look, the weight of the object is only 490N, so if the string is parallel to the surface, the tension and the normal force must each be less than 490N. (And if the string is not parallel to the surface, we need more info -- such as the height of the object and the point of attachment of the string).
 
  • #3
Thanks for your help. But, what you said about the answers being less than 508 is exactly what I was thinking. Unfortunately the answers in the back of my textbook lists that both values are 508 Newtons. I checked several times that these answers were indeed referring to the correct problem and chapter, and they are. In addition, the string is parallel to the inclined plane and no height is given for the object or the plane. Perhaps the answer in the back is wrong. I found the right answer for all of the other problems that I tried. I'll just have to ask my teacher about this one.

Thanks again.
 
  • #4
My teacher announced today that the answers in the back of the book are indeed wrong. The answers that I was getting of 425N and 245N turned out to be correct.
 

1. How do you calculate the normal force and tension in a string?

To calculate the normal force, you need to first identify the object that is exerting the force on the string. Then, you can use the formula F = ma, where F is the normal force, m is the mass of the object, and a is the acceleration due to gravity (9.8 m/s^2). To calculate the tension in the string, you can use the formula T = mg + ma, where T is the tension, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object (if any).

2. What is the difference between normal force and tension in a string?

The normal force is the force exerted by a surface on an object that is in contact with it, perpendicular to the surface. In the case of a string, the normal force would be the force exerted by the string on an object that is hanging from it. Tension, on the other hand, is the force exerted by the string on the object that is causing it to stretch or pull. In other words, the normal force keeps an object from falling through a surface, while tension keeps an object from breaking the string.

3. What factors affect the normal force and tension in a string?

The normal force is affected by the mass of the object and the acceleration due to gravity, while the tension is affected by the mass of the object, the acceleration due to gravity, and the acceleration of the object (if any). Additionally, the length and stiffness of the string can also affect the tension.

4. Can the normal force or tension ever be negative?

No, the normal force and tension can never be negative. The normal force always acts in the opposite direction of the force that is pushing down on the surface, and tension is always a positive value since it represents the force exerted by the string.

5. How is the normal force and tension related to each other?

The normal force and tension are directly related since they both involve the force exerted by the string on an object. As the tension increases, the normal force also increases, since the string needs to exert a greater force to keep the object from falling through the surface. Similarly, as the tension decreases, the normal force also decreases.

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