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Chapter 12: Q61P (page 351)

The force F→ in Fig. 12-70 keeps the 6.40 kg 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 N.

Step by step solution

01

Understanding the given information

Mass of the block, m=6.40 kg

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.

∑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 N

We can write,

T1+T2+T3=mg7F=mgF=mg7F=62.72 N7F=8.96 N

We already found that,

T=8F

So,

T=(8.96 N)(8)=71.68 N

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

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Most popular questions from this chapter

Figure 12-62 is an overhead view of a rigid rod that turns about a vertical axle until the identical rubber stoppersAand Bare forced against rigid walls at distancesrA=7.0cmandrB=4.0cmfrom the axle. Initially the stoppers touch the walls without being compressed. Then forceFof magnitude 220Nis applied perpendicular to the rod at a distance R=5.0cmfrom the axle. Find the magnitude of the force compressing (a) stopperA, and (b) stopper.B

In Fig. 12-60, a 103 kguniform log hangs by two steel wires, Aand B, both of radiuses 1.20 mm. Initially, wire Awas 2.50 mlong and 2.0 mmshorter than wire B. The log is now horizontal. What are the magnitudes of the forces on it from (a) wire Aand (b) wire B? (c) What is the ratio dA/dB?

Question: Fig. 12-31 shows the anatomical structures in the lower leg and foot that are involved in standing on tiptoe, with the heel raised slightly off the floor so that the foot effectively contacts the floor only at point P. Assume distance a = 0 .5 cm , distanceb = 15 cm, and the person’s weight W = 900 N. Of the forces acting on the foot, what are the (a) magnitude and (b) direction (up or down) of the force at point Afrom the calf muscle and the (c) magnitude and (d) direction (up or down) of the force at point Bfrom the lower leg bones?

In Fig. 12-44, a 15 kg block is held in place via a pulley system. The person’s upper arm is vertical; the forearm is at angleθ=30o with the horizontal. Forearm and hand together have a mass of 2.0 kg, with a center of mass at distance d1=15 cmfrom the contact point of the forearm bone and the upper-arm bone(humerus). The triceps muscle pulls vertically upward on the forearm at distanced2=2.5 cm behind that contact point. Distanced3is 35 cm. What are the (a)magnitude and (b) direction (up or down) of the force on the forearm from the triceps muscle and the (c) magnitude and (d) direction (up or down) of the force on the forearm from the humerus?

In Fig. 12-73, a uniform beam with a weight of 60 Nand a length of 3.2 m 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 θ=25°with the ground and is attached to the beam at height h=2.0 m . What are (a) the tension in the cable and (b) the force on the beam from the hinge in unit-vector notation?
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