Tension on a string attached to two objects

In summary: Thank youIn summary, the question asks for the force that the chain can exert on the car when a person is pulling on it perpendicular to its length. Using basic trigonometry, the person can calculate the angle between the base and hypotenuse of two congruent triangles formed by connecting a line from the person to the ground. With this angle, the force exerted by the chain on the car can be calculated to be 364 N, which is twice the value given by the book. Additionally, the question of how many forces are acting on the person and the chain is discussed, with the conclusion that there are three forces in total. The presence of friction is also considered, but it is ultimately determined to have no effect on the final
  • #1
unified
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0

Homework Statement


A person would like to pull a car out of a ditch. This person ties one end of a chain to the car's bumper and wraps the other end around a tree so that the chain is taut. The person then pulls on the chain perpendicular to its length. If the distance between the car and tree is 5.0 m and the length of the chain between the car and the tree is 5.2 m and the person can pull with 100LB of force, what force can the chain exert on the car?

Homework Equations


Basic trigonometry

The Attempt at a Solution



Let d_1, d_2 be 5.0 m and 5.2 m respectively. Let F_1 be 100 LB.
Draw a pair of congruent triangles by connecting a line from the person to the ground. This gives two right triangles with base (1/2)d_1 and hypotenuse (1/2)d_2. You can calculate the angle between the base and hypotenuse to be about 15.94 degrees which we may call theta. Then F_T = csc(theta) * F_1 = 364 N. The book gets about half of that at 180 N.
 
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  • #2
unified said:

Homework Statement


A person would like to pull a car out of a ditch. This person ties one end of a chain to the car's bumper and wraps the other end around a tree so that the chain is taut. The person then pulls on the chain perpendicular to its length. If the distance between the car and tree is 5.0 m and the length of the chain between the car and the tree is 5.2 m and the person can pull with 100LB of force, what force can the chain exert on the car?

Homework Equations


Basic trigonometry

The Attempt at a Solution



Let d_1, d_2 be 5.0 m and 5.2 m respectively. Let F_1 be 100 LB.
Draw a pair of congruent triangles by connecting a line from the person to the ground. This gives two right triangles with base (1/2)d_1 and hypotenuse (1/2)d_2. You can calculate the angle between the base and hypotenuse to be about 15.94 degrees which we may call theta. Then F_T = csc(theta) * F_1 = 364 N. The book gets about half of that at 180 N.
Consider the point on the chain where the person is pulling. Draw an FBD for that. How many forces are there?
 
  • #3
haruspex said:
Consider the point on the chain where the person is pulling. Draw an FBD for that. How many forces are there?

Of course I've done that. If we ignore the frictional forces with the ground as the book usually does in a situation like this, and cancel the gravitational and normal forces, there are two forces acting on the person along the two chains.
 
  • #4
unified said:
Of course I've done that. If we ignore the frictional forces with the ground as the book usually does in a situation like this, and cancel the gravitational and normal forces, there are two forces acting on the person along the two chains.
haruspex said:
Consider the point on the chain where the person is pulling. Draw an FBD for that. How many forces are there?

On second thought, I don't think I should ignore the frictional force with the ground. The frictional force with the ground is acting say downward, and for static equilibrium, the upward forces from the chains have to cancel, and I think I get the right answer this way. Is that how you thought about it?
 
  • #5
unified said:
Of course I've done that. If we ignore the frictional forces with the ground as the book usually does in a situation like this, and cancel the gravitational and normal forces, there are two forces acting on the person along the two chains.
Ok, but I would prefer to view it as those two forces, each FT, plus the pull F1 from the person all acting at a point on the chain. So that gives three forces altogether. Consider the force balance in the direction in which the person pulls.
 
  • #6
unified said:
On second thought, I don't think I should ignore the frictional force with the ground. The frictional force with the ground is acting say downward, and for static equilibrium, the upward forces from the chains have to cancel, and I think I get the right answer this way. Is that how you thought about it?
There's no indication that the chain remains in contact with the ground. It would be unlikely. Anyway, there would be no normal force from the ground, so no friction.
 
  • #7
OK, I see your point. The friction argument shouldn't matter anyways, because the result still holds in a friction free environment. Of course what I meant was the net forces acting on the person, so friction from the ground plus the two Tensions all sum to 0. But, I like the way you are reasoning here.
 

1. How does tension on a string work?

When a string is attached to two objects, tension is the force that is transmitted through the string. This means that if one end of the string is pulled, the other end will also experience a force in the opposite direction. This creates tension on the string, which is responsible for keeping the objects connected and preventing them from moving apart.

2. What factors affect the tension on a string?

The tension on a string is affected by several factors, including the weight of the objects attached to the string, the length of the string, and the angle at which the string is pulled. The greater the weight of the objects, the longer the string, or the sharper the angle, the greater the tension on the string will be.

3. Can the tension on a string be greater than the weight of the objects attached to it?

Yes, the tension on a string can be greater than the weight of the objects attached to it. This is because the tension on the string is not only determined by the weight of the objects, but also by the other factors mentioned in the previous answer. So, even if the weight of the objects is relatively small, the tension on the string can still be significant if the other factors are high.

4. What happens when the tension on a string is too high?

If the tension on a string becomes too high, it can cause the string to break or the objects attached to the string to move apart. This is because the string can only withstand a certain amount of tension before it reaches its breaking point. It is important to consider the maximum tension a string can handle in order to prevent accidents or damage.

5. How can the tension on a string be calculated?

The tension on a string can be calculated using the formula T = F * sin(theta), where T is the tension, F is the force applied to one end of the string, and theta is the angle at which the string is pulled. This formula takes into account the weight of the objects, the angle of the string, and the gravitational force acting on the objects. Alternatively, the tension can also be calculated by measuring the elongation of the string when a certain weight is attached to it.

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