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Chapter 12: Q12P (page 346)

Question: In Fig 12-30, trying to get his car out of mud, a man ties one end of a rope around the front bumper and the other end tightly around a utility pole 18 maway. He then pushes sideways on the rope at its midpoint with a force of 550 N , displacing the center of the rope 0.30 m, but the car barely moves. What is the magnitude of the force on the car from the rope? (The rope stretches somewhat.)

Short Answer

Expert verified

Answer:

Magnitude of force on the car from the rope is 8.3脳103N.

Step by step solution

01

Understanding the given information

F = 550 N

Displacement of the center of the rope is0.30 m .

02

Concept and formula used in the given question 

By drawing an FBD of the rope, you can calculate the angle by using the given geometry. By applying static equilibrium conditions, you can get the tensions on the both sides of rope. Then by solving the torque equation, you can calculate the tension on the rope by using the formula given below.

Static Equilibrium conditions:

鈭�Fx=0鈭�Fy=0鈭�蟿=0

03

Calculation for the magnitude of the force on the car from the rope

FBD of the rope:

From the figure,

胃=tan-10.39=1.90鈭�Fx=0T1脳cos胃-T2脳cos胃=0

Hence,

T1=T2=T鈭�Fy=02T脳sin胃-F=02T脳sin1.9-550=0

By solving for T:

T=8300N=8.3脳103N

Hence, theMagnitude of force on the car from the rope is8.3脳103N .

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Most popular questions from this chapter

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?

Question: A bowler holds a bowling ball (M = 7.2 Kg) in the palm of his hand (Figure 12-37). His upper arm is vertical; his lower arm (1.8 kg) is horizontal. What is the magnitude of (a) the force of the biceps muscle on the lower arm and (b) the force between the bony structures at the elbow contact point?

The Figure represents an insect caught at the midpoint of a spider-web thread. The thread breaks under a stress of 8.20脳108鈥�N/m2and a strain of 2.00. Initially, it was horizontal and had a length of 2.00cm and a cross-sectional area of 8.00脳10鈭�12m2. As the thread was stretched under the weight of the insect, its volume remained constant. If the weight of the insect puts the thread on the verge of breaking, what is the insect鈥檚 mass? (A spider鈥檚 web is built to break if a potentially harmful insect, such as a bumble bee, becomes snared in the web.)

The system in Fig. 12-38 is in equilibrium. A concrete block of mass225kghangs from the end of the uniform strut of mass45.0kg. A cable runs from the ground, over the top of the strut, and down to the block, holding the block in place. For angles蠒=30.0掳and胃=45.0掳, find (a) the tension Tin the cable and the (b) horizontal and (c) vertical components of the force on the strut from the hinge.

In Fig. 12-20, a stationary 5 kg rod ACis held against a wall by a rope and friction between rod and wall. The uniform rod is 1 m long, and angle

(a) If you are to find the magnitude of the force T鈫�
on the rod from the rope with a single equation, at what labeled point should a rotation axis be placed? With that choice of axis and counter-clockwise torques positive,

what is the sign of

(b) the torque蟿wdue to the rod鈥檚 weight and

(c) the torque蟿rdue to the pull on the rod the rope?

(d) Is the magnitude of 蟿rgreater than, less than, or equal to the magnitude of 蟿w?
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