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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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