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Chapter 12: Q61P (page 351)

The force F鈫� in Fig. 12-70 keeps the 6.40鈥塳驳 block and the pulleys in equilibrium. The pulleys have negligible mass and friction. Calculate the tension Tin the upper cable. (Hint:When a cable wraps halfway around a pulley as here, the magnitude of its net force on the pulley is twice the tension in the cable.)

Short Answer

Expert verified

Tension T in the upper cable is 71.68鈥塏.

Step by step solution

01

Understanding the given information

Mass of the block, m=6.40鈥塳驳

02

Concept and formula used in the given question

Using the equilibrium conditions, you can write the equations for force for the lowest pulley and find the tension in terms of applied force. You can do it for the remaining two pulleys and find the tension in the string holding the topmost pulley. The formula used is given below.

鈭�Fnet=0

03

Calculation for the tension T in the upper cable

From the figure, we can conclude that

T1=FT2=F+T1T2=2FT3=2F+T2T3=4FT=4F+T3T=8F

In addition, we know the value of force,F=62.72鈥塏

We can write,

T1+T2+T3=mg7F=mgF=mg7F=62.72鈥�N7F=8.96鈥塏

We already found that,

T=8F

So,

T=(8.96鈥�N)(8)=71.68鈥塏

Thus, the tension in the upper cable is 71.68鈥塏.

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Most popular questions from this chapter

In Fig. 12-73, a uniform beam with a weight of 60鈥塏and a length of 3.2鈥尘 is hinged at its lower end, and a horizontal force of magnitude 50 N acts at its upper end. The beam is held vertical by a cable that makes angle 胃=25掳with the ground and is attached to the beam at height h=2.0鈥尘 . What are (a) the tension in the cable and (b) the force on the beam from the hinge in unit-vector notation?

A uniform beam is 5.0鈥尘long and has a mass of 53鈥塳驳. In Fig. 12-74, the beam is supported in a horizontal position by a hinge and a cable, with angle胃=60掳. In unit-vector notation, what is the force on the beam rom the hinge?

A ladder leans against a frictionless wall but is prevented from falling because of friction between it and the ground. Suppose you shift the base of the ladder toward the wall. Determine whether the following become larger, smaller, or stay the same (inmagnitude):

(a) the normal force on the ladder from the ground,

(b) the force on the ladder from the wall,

(c) the static frictional force on the ladder from the ground, and

(d) the maximum value Fs,max of the static frictional force.

Figure 12-84 shows a stationary arrangement of two crayon boxes and three cords. Box Ahas a mass of11.0鈥塳驳 and is on a ramp at angle 胃=30.0掳box Bhas a mass of7.00鈥塳驳 and hangs on a cord. The cord connected to box Ais parallel to the ramp, which is frictionless. (a) What is the tension in the upper cord, and (b) what angle does that cord make with the horizontal?

In Fig. 12-69, a package of mass mhangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle蠒=40掳with the horizontal; cord 2 is at angle胃. (a) For what value of 胃is the tension in cord 2 minimized? (b) In terms of mg, what is the minimum tension in cord 2
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