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Chapter 8: Q.39 (page 200)
A man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much? Assume the earth is spherical.
The weight at the north pole is larger by .
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Suppose you swing a ball of mass m in a vertical circle on a string of length L. As you probably know from experience, there is a minimum angular velocity 蝇min you must maintain if you want the ball to complete the full circle without the string going slack at the top.
a. Find an expression for 蝇min
b. Evaluate蝇minin rpm for a 65 g ball tied to a 1.0-m-long string.
The 10 mg bead in FIGURE P8.48 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity 蝇. If 蝇 is less than some critical value 蝇c the bead sits at the bottom of the spinning loop. When 蝇 > 蝇c the bead moves out to some angle 胃
conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. FIGURE P8.47 shows that the string traces out the surface of a cone, hence the name.
a. Find an expression for the tension T in the string.
b. Find an expression for the ball鈥檚 angular speed v.
c. What are the tension and angular speed (in rpm) for a 500 g ball swinging in a 20-cm-radius circle at the end of a 1.0-m-long string?
A block on a -long string swings in a circle on a horizontal, frictionless table at .
a. What is the speed of the block?
b. What is the tension in the string?
While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be , and you use your watch to find that each loop around takes .
a. What are your speed and the magnitude of your acceleration?
b. What is the ratio of your weight at the top of the ride to your weight while standing on the ground?
c. What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground?
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