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Chapter 8: Q.24 (page 199)
A ball swings in a vertical circle at the end of a -long string. When the ball is at the bottom of the circle, the tension in the string is . What is the speed of the ball at that point?
The speed of the ball at that point is.
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The physics of circular motion sets an upper limit to the speed of human walking. (If you need to go faster, your gait changes from a walk to a run.) If you take a few steps and watch
what’s happening, you’ll see that your body pivots in circular motion over your forward foot as you bring your rear foot forward for the next step. As you do so, the normal force of the
ground on your foot decreases and your body tries to “lift off” from the ground.
a. A person’s center of mass is very near the hips, at the top of the legs. Model a person as a particle of mass m at the top of a leg of length L. Find an expression for the person’s maximum walking speed vmax.
b. Evaluate your expression for the maximum walking speed of a 70 kg person with a typical leg length of 70 cm. Give your answer in both m/s and mph, then comment, based on your
experience, as to whether this is a reasonable result. A “normal” walking speed is about 3 mph.
In an old-fashioned amusement park ride, passengers stand inside a-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly
drops away! If all goes well, the passengers will “stick” to the wall and not slide. Clothing has a static coefficient of friction against steel in the range to and a kinetic coefficient in the rangeto A sign next to the entrance says “No children under allowed.” What is the minimum angular speed, in rpm, for which the ride is safe?
Sam (75 kg) takes off up a 50-m-high, 10 frictionless slope on his jet-powered skis. The skis have a thrust of 200 N. He keeps his skis tilted at 10o after becoming airborne, as shown in FIGURE CP8.66. How far does Sam land from the base of the cliff?
A jet plane is flying on a level course at constant speed. The engines are at full throttle.
a. What is the net force on the plane? Explain.
b. Draw a free-body diagram of the plane as seen from the side with the plane flying to the right. Name (don’t just label) any and all forces shown on your diagram.
c. Airplanes bank when they turn. Draw a free-body diagram of the plane as seen from behind as it makes a right turn.
d. Why do planes bank as they turn? Explain.
If a vertical cylinder of water (or any other liquid) rotates about its axis, as shown in FIGURE CP8.71, the surface forms a smooth curve. Assuming that the water rotates as a unit (i.e., all the water rotates with the same angular velocity), show that the shape of the surface is a parabola described by the equation
Hint: Each particle of water on the surface is subject to only two forces: gravity and the normal force due to the water underneath it. The normal force, as always, acts perpendicular to the surface.
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