Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 56 | Concept Questions Interactive LearningWare 5.1 at explores how to solve problems that have concepts similar to this one. The second hand and the minute hand on one type of clock are the same length. What is the period T of the motion for (a) the second hand and (b) the minute hand? (c) We have seen that the centripetal acceleration is given by where v is the speed and r is the radius. How is the centripetal acceleration related to the period? In each case, explain your reasoning.
Problem Find the ratio (ac, second/ac, minute) of the centripetal accelerations for the tips of the second hand and the minute hand.

| 57 | Concept Questions The following table lists data for the speed and the radius in three examples of uniform circular motion.

| Radius | Speed
Example 1 | 0.50 m | 12 m/s
Example 2 | Infinitely large | 35 m/s
Example 3 | 1.8 m | 2.3 m/s

(a) Without doing any calculations, identify the example with the smallest centripetal acceleration. (b) Similarly identify the example with the greatest centripetal acceleration. In each case, justify your answer.
Problem Find the value for the centripetal acceleration for each example. Verify that your answers are consistent with your answers to the Concept Questions.

| 58 | Concept Questions Interactive LearningWare 5.2 at illustrates good problem-solving techniques for this type of problem. Two cars are traveling at the same speed of 27 m/s on a curve that has a radius of 120 m. Car A has a mass of 1100 kg, and car B has a mass of 1600 kg. Without doing any calculations, decide (a) which car, if either, has the greater centripetal acceleration and (b) which car, if either, experiences the greater centripetal force. Justify your answers.
Problem Find the centripetal acceleration and the centripetal force for each car. Be sure that your answers are consistent with your answers to the Concept Questions.

| 59 | Concept Questions Multiple-Concept Example 7 deals with the concepts that are important in this problem. A penny is placed at the outer edge of a disk (radius = 0.150 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.80 s. (a) What is producing the centripetal force that enables the penny to rotate along with the disk—kinetic or static friction? (b) The centripetal force needed depends on the speed at which the penny is moving. On what does this speed depend? Account for your answer in each case.
Problem Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk.

| 60 | Concept Questions Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 360 km above the earth’s surface, while that for satellite B is at a height of 720 km. (a) Which satellite has the greater orbital speed? (b) The speed of a satellite in a circular orbit is given by Equation 5.5 . In this expression, do you substitute the heights of and for the term r? Explain your answers.
Problem Find the orbital speed for each satellite. Check to see that your answers are consistent with your answers to the Concept Questions.

| 61 | Concept Questions A 0.20-kg ball on a string is whirled on a vertical circle at a constant speed. When the ball is at the three o’clock position, the tension is 16 N. (a) Is the centripetal force acting on the ball the same at each point on the circle? (b) When the ball is at the three o’clock position, what is providing the centripetal force—gravity, the tension in the string, or a combination of both? (c) Is the tension in the string greater when the ball is at the twelve o’clock position or when it is at the six o’clock position? Justify your answers.
Problem Find the tensions in the string when the ball is at the twelve o’clock and at the six o’clock positions. Verify that your answers are consistent with your answers to the Concept Questions.

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