Problem Set 4

Reading for this coming week is Chapter 6. It is best to read the chapter before the class and re-read it afterwards. As a reminder, the first mid-term exam will be during the first week in October.

(1) Ch 5 P 3 (I) Calculate the centripetal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? [Hint: see the Tables inside the front cover of this book.]

(2) Ch 5 P 7 (II) A ball on the end of a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm, as shown in Fig. 5–33. If its speed is 4.00 m/s and its mass is 0.300 kg, calculate the tension in the string when the ball is (a) at the top of its path, and (b) at the bottom of its path.

(3) Ch 5 P 8 (II) A 0.45-kg ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N, what is the maximum speed the ball can have?

(4) Ch 5 P 10 (II) How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95 km/hr ?

(5) Ch 5 P 13 (II) At what minimum speed must a roller coaster be traveling when upside down at the top of a circle (Fig. 5–34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.

(7) Ch 5 P 18 (II) In a “Rotor-ride” at a carnival, people are rotated in a cylindrically walled “room.” (See Fig. 5–35.) The room radius is 4.6 m, and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were “pressed against the wall.” Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides “scary”)? [Hint: First draw the free-body diagram for a person.]

(8) Ch 5 P 19 (II) A flat puck (mass M) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m) through a central hole as shown in Fig. 5–36. Show that the speed of the puck is given by v^2 = mgR/M .

(9) Ch 5 P 65 [As in Larry Niven's Ringworld] A science-fiction tale describes an artificial “planet” in the form of a band completely encircling a sun (Fig. 5–40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth–Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet’s year, in Earth days?

(10) Ch 5 P 67 How far above the Earth’s surface will the acceleration of gravity be half what it is on the surface? Feel free to express you answer in terms of the radius of the earth.

(11) Ch 5 P 94 Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of 160 km/hr (approximately 100 mph). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. (b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.