Force applied on cable attached to car and tree

In summary, a car stuck in the mud can be pulled out by connecting a long cable between the car's front bumper and a tree trunk, and pulling sideways on the cable at its midpoint with a force f. The force acting on the car can be determined using the equations Efx=0 and Efy=0, resulting in an equation for F=2tsin@. When solving for T, the angle must be denoted as "u". A different method involves drawing a free body diagram and solving for the force at the point where f is applied.
  • #1
Ab17
99
2

Homework Statement


your car is stuck in the mud and you can’t pull hard enough to get it out. You do, however, have a long cable that you connect taut between your front bumper and the trunk of a stout tree. You now pull sideways on the cable at its midpoint, exerting a force f. Each half of the cable is displaced through a small angle u from the straight line between the ends of the cable. (a) Deduce an expression for the force acting on the car. (b) Evaluate the cable tension for thecasewhereu57.00°andf 5100N

Homework Equations


Efx=0
Efy=O

The Attempt at a Solution



Efx
T1cos@ = t2cos@
T1=T2
Efy=0
F = 2tsin@

Is this right?
 
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  • #2
Ab17 said:
F = 2tsin@

Close. That's an equation for F.

The angle is defined in the problem as "u" rather than "@".
 
  • #3
But is the method of solution correct besides the u?
 
  • #4
Your answer is correct if you rearrange it to give an equation for T.

I don't understand your method.
 
  • #5
I would solve it by drawing a fbd for the point on the rope where f Is applied.
 

Related to Force applied on cable attached to car and tree

1. What is the force applied on the cable attached to the car and tree?

The force applied on the cable attached to the car and tree would depend on the tension in the cable and the angle at which it is attached to both the car and the tree. It can be calculated using the formula F = T x sin(theta), where F is the force, T is the tension, and theta is the angle between the cable and the horizontal.

2. How does the angle at which the cable is attached affect the force applied?

The angle at which the cable is attached to the car and tree will affect the force applied. As the angle increases, the force applied will also increase. This is because a greater angle means a greater component of the tension force is acting in the direction of the car, resulting in a larger force on the cable.

3. What factors influence the tension in the cable?

The tension in the cable is influenced by several factors, including the weight of the car, the angle at which the cable is attached, and any external forces acting on the cable, such as wind resistance or friction. The type and strength of the cable itself can also affect the tension.

4. Can the force applied on the cable be greater than the tension in the cable?

Yes, it is possible for the force applied on the cable to be greater than the tension in the cable. This can happen if there are additional external forces acting on the cable, such as strong winds or a sudden impact, which can increase the overall force on the cable beyond the tension force.

5. Why is it important to consider the force on the cable in this scenario?

Considering the force on the cable is important because it can help determine the stability and safety of the car and tree. If the force applied on the cable exceeds the tension in the cable, it could potentially cause damage or even lead to the car or tree falling. Understanding the force on the cable can also help with proper installation and maintenance of the cable.

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