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This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let Fu and Fd (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless so that its weight is negligible compared with the tension. (This is not a ridiculous approximation-modern rope material such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.)

Consider the three sections of rope labeled a, b, and c in the figure.

  • At point 1, a downward force of magnitude Fad acts on section a.
  • At point 1, an upward force of magnitude Fbu acts on section b.
  • At point 1, the tension in the rope is T1.
  • At point 2, a downward force of magnitude Fbd acts on section b.
  • At point 2, an upward force of magnitude Fcu acts on section c.
  • At point 2, the tension in the rope is T2.

(A) What is the magnitude Fad of the downward force on section a?

(B) What is the magnitude Fbu of the upward force on section b?

(C) The magnitude of the upward force on c, Fcu, and the magnitude of the downward force on b, Fbd, are equal because of which of Newton's laws?

(D) The magnitude of the force Fbu is ______ Fbd.

(E) Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces?

(a) Fu > Fd

(b) Fu = Fd

(c) Fu < Fd

(F) The ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line. For this situation, which of the following statements are true?

(a) The tension in the rope is everywhere the same.

(b) The magnitudes of the forces exerted on the two objects by the rope are the same.

(c) The forces exerted on the two objects by the rope must be in opposite directions.

(d) The forces exerted on the two objects by the rope must be in the direction of the rope.

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Rochelle Enrera
Rochelle EnreraLv10
6 Jan 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

If your car is stuck in the mud and you don’t have a winch to pullit out, you can use a piece of rope and a tree to do the trick.First, you tie one end of the rope to your car and the other to atree, then pull as hard as you can on the middle of the rope, asshown in the figure. This technique applies a force to the car muchlarger than the force that you can apply directly. To see why thecar experiences such a large force, look at the forces acting onthe center point of the rope, as shown in the figure. The sum ofthe forces is zero, thus the tension is much greater than the forceyou apply. It is this tension force that acts on the car and, withluck, pulls it free.

1.) The sum of the three forces acting on the center point of therope is assumed to be zero because
a.) this point has a very small mass
b.) tension forces in a rope always cancel
c.) this point is not accelerating
d.) the angle of deflection is very small.

2.) when you are pulling on the rope what is the approximatedirection of the tension force on the tree?
a.) north b.) south c.) east d.) west

3.) assume that you are pulling on the rope but the car is notmoving. what is the approximate direction of the force of the mudon the car?
a.) north b.) south c.) east d.) west

4.) suppose your efforts work, and the car begins to move forwardout of the mud. As it does so, the force of the car on the ropeis
a.) zero
b.) less than the force of the rope on the car
c.) equal to the force of the rope on the car
d.) greater than the force of the rope on the car.

  • If your car is stuck in the mud and you don’t have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in the figure. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in the figure. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free.

    1.) The sum of the three forces acting on the center point of the rope is assumed to be zero because
    a.) this point has a very small mass
    b.) tension forces in a rope always cancel
    c.) this point is not accelerating
    d.) the angle of deflection is very small.

    2.) when you are pulling on the rope what is the approximate direction of the tension force on the tree?
    a.) north b.) south c.) east d.) west

    3.) assume that you are pulling on the rope but the car is not moving. what is the approximate direction of the force of the mud on the car?
    a.) north b.) south c.) east d.) west

    4.) suppose your efforts work, and the car begins to move forward out of the mud. As it does so, the force of the car on the rope is
    a.) zero
    b.) less than the force of the rope on the car
    c.) equal to the force of the rope on the car
    d.) greater than the force of the rope on the car.

The system shown is used to lift an object of mass m = 76.0 kg. A constant downward force of magnitude F is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rope and pulleys, find (a) the required value of F, (b) the tensions T1, T2, and T3, and (c) the work done by the applied force in raising the object a distance of 1.80 m.

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