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6 - Circular Motion and Other Applications of Newton's Laws

# Angle that gives the maximum range for the projectile

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Unformatted text preview: the ball? Discuss the differences in trajectories between the two shots. ADDITIONAL PROBLEMS 46. An 1 800-kg car passes over a bump in a road that follows the arc of a circle of radius 42.0 m as in Figure P6.46. (a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 16.0 m/s? (b) What is the maximum speed the car can have as it passes this highest point before losing contact with the road? 47. A car of mass m passes over a bump in a road that follows the arc of a circle of radius R as in Figure P6.46. (a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at a speed v ? (b) What is the maximum speed the car can have as it passes this highest point before losing contact with the road? v Figure P6.46 Problems 46 and 47. 48. In one model of a hydrogen atom, the electron in orbit around the proton experiences an attractive force of about 8.20 10 8 N. If the radius of the orbit is 5.30 10 11 m, how many revolutions does the electron make each second? (This number of revolutions per unit time is called the frequency of the motion.) See the inside front cover for additional data. 49. A student builds and calibrates an accelerometer, which she uses to determine the speed of her car around a certain unbanked highway curve. The accelerometer is a plumb bob with a protractor that she attaches to the roof of her car. A friend riding in the car with her observes that the plumb bob hangs at an angle of 15.0° from the vertical when the car has a speed of 23.0 m/s. (a) What is the centripetal acceleration of the car rounding the curve? (b) What is the radius of the curve? (c) What is the speed of the car if the plumb bob deﬂection is 9.00° while the car is rounding the same curve? 50. Suppose the boxcar shown in Figure 6.13 is moving with constant acceleration a up a hill that makes an angle with the horizontal. If the hanging pendulum makes a constant angle with the perpendicular to the ceiling, what is a ? 51. An air puck of mass 0.250 kg is tied to a string and allowed to revolve in a circle of radius 1.00 m on a fric- 178 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws tionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.00 kg is tied to it (Fig. P6.51). The suspended mass remains in equilibrium while the puck on the tabletop revolves. What are (a) the tension in the string, (b) the force exerted by the string on the puck, and (c) the speed of the puck? 52. An air puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass m 2 is tied to it (Fig. P6.51). The suspended mass remains in equilibrium while the puck on the tabletop revolves. What are (a) the tension in the string? (b) the central force exerted on th...
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