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 ball is held in hands and balanced. It is neither moving linearly nor rotating about any pivot point. So, it is in static equilibrium condition. By selecting a pivot point and applying the static equilibrium conditions, you can write the torque equation in terms of force and distance. Solving this equation, you would get the unknown tension and force.
Using the figure given in the problem and condition of static equilibrium, we can write torque and force equations as,
Substitute the values in equation 1, and we get,
Hence, the magnitude of the force of the bicep muscle on the lower arm is .
Substitute the values in equation 2, and we get,
Hence, the force between the bony structures at the elbow contact point is .
The system in Fig. 12-38 is in equilibrium. A concrete block of mass hangs from the end of the uniform strut of mass. A cable runs from the ground, over the top of the strut, and down to the block, holding the block in place. For angles and , find (a) the tension T in the cable and the (b) horizontal and (c) vertical components of the force on the strut from the hinge.
Figure 12-17 shows four overhead views of rotating uniform disks that are sliding across a frictionless floor. Three forces, of magnitude F, 2F , or 3F, act on each disk, either at the rim, at the center, or halfway between rim and center. The force vectors rotate along with the disks, and, in the “snapshots” of Fig. 12-17, point left or right. Which disks are in equilibrium?
A cylindrical aluminum rod, with an initial length of and radius , is clamped in place at one end and then stretched by a machine pulling parallel to its length at its other end. Assuming that the rod’s density (mass per unit volume) does not change, find the force magnitude that is required of the machine to decrease the radius to . (The yield strength is not exceeded.)
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