Take up as positive and down as negative.

**Part A**

The acceleration is zero at equilibrium.

ΣF = ma

T_{1} - F_{ad} = 0

To understand the concept of tension and the relationship between tension and force. This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. (Figure 1)

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 materials 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 F_{ad} acts on section a.

At point 1, an upward force of magnitude F_{bu} acts on section b.

At point 1, the tension in the rope is T_{1}.

At point 2, a downward force of magnitude F_{bd} acts on section b.

At point 2, an upward force of magnitude F_{cu} acts on section c.

At point 2, the tension in the rope is T_{2}. Assume, too, that the rope is at equilibrium.

Part A

What is the magnitude *F*_{ad} of the downward force on section a?

Express your answer in terms of the tension *T*_{1}.

Part B

What is the magnitude *F*_{bu} of the upward force on section b?

Express your answer in terms of the tension *T*_{1}.

Part C

The magnitude of the upward force on c, *F*_{cu}, and the magnitude of the downward force on b, *F*_{bd}, are equal because of which of Newton's laws?

Part D

The magnitude of the force *F*_{bu} is ____ *F*_{bd}.

Part E

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

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

*a) F** _{u} *>

*b) F*_{u} <*F*_{d}

*c) F*_{u} =*F*_{d}

Part 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?

Check all that apply.

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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