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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 8.3×103N.

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:

∑Fx=0∑Fy=0∑τ=0

03

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

FBD of the rope:

From the figure,

θ=tan-10.39=1.90∑Fx=0T1×cosθ-T2×cosθ=0

Hence,

T1=T2=T∑Fy=02T×sinθ-F=02T×sin1.9-550=0

By solving for T:

T=8300N=8.3×103N

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

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Most popular questions from this chapter

Question: In Figure 12-40, one end of a uniform beam of weight is hinged to a wall; the other end is supported by a wire that makes angles θ=30o with both wall and beam. (a) Find the tension in the wire and the (b) Find horizontal and (c) Find vertical components of the force of the hinge on the beam.

Figure (a) shows a horizontal uniform beam of massmband lengthLthat is supported on the left by a hinge attached to a wall and on theright by a cable at angle θ with the horizontal. A package of mass mp is positioned on the beam at a distance x from the left end. The total mass ismb+mp=61.22kg. Figure (b) gives the tension T in the cable as a function of the package’s position given as a fraction x/L of the beam length. The scale of the T axis is set by Ta=500N and Tb=700N.

(a) Evaluate angleθ ,

(b) Evaluate massmb , and

(c) Evaluate mass mp.

Question: To crack a certain nut in a nutcracker, forces with magnitudes of at least 40 N must act on its shell from both sides. For the nutcracker of Figure, with distances L =12 cmand D = 2.6 cm , what are the force components F⊥ (perpendicular to the handles) corresponding to that 40 N?

A mine elevator is supported by a single steel cable2.5cmin diameter. The total mass of the elevator cage and occupants is670kg .By how much does the cable stretch when the elevator hangs by (a)12m of cableand (b) 362mof cable?(Neglect the mass of the cable.)

In Figure 12-43, a climber leans out against a vertical ice wall that has negligible friction. Distance ais 0.914 m and distance Lis2.10 m. His center of mass is distance d=0.940 mfrom the feet–ground contact point. If he is on the verge of sliding, what is the coefficient of static friction between feet and ground?
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