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 m away. 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.)
Magnitude of force on the car from the rope is .
F = 550 N
Displacement of the center of the rope is 0.30 m .
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:
FBD of the rope:
From the figure,
By solving for T:
Hence, the Magnitude of force on the car from the rope is .
Figure 12-85a shows details of a finger in the crimp hold of the climber in Fig. 12-50. A tendon that runs from muscles in the forearm is attached to the far bone in the finger. Along the way, the tendon runs through several guiding sheaths called pulleys. The A2 pulley is attached to the first finger bone; the A4 pulley is attached to the second finger bone. To pull the finger toward the palm, the forearm muscles pull the tendon through the pulleys, much like strings on a marionette can be pulled to move parts of the marionette. Figure 12-85b is a simplified diagram of the second finger bone, which has length d. The tendon’s pull on the bone acts at the point where the tendon enters the A4 pulley, at distance d/3 along the bone. If the force components on each of the four crimped fingers in Fig. 12-50 are and , what is the magnitude of ? The result is probably tolerable, but if the climber hangs by only one or two fingers, the A2 and A4 pulleys can be ruptured, a common ailment among rock climbers.
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 angle with the horizontal. Forearm and hand together have a mass of 2.0 kg, with a center of mass at distance from the contact point of the forearm bone and the upper-arm bone(humerus). The triceps muscle pulls vertically upward on the forearm at distance behind that contact point. Distance is 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?
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