Deck 8: Dynamics Ii: Motion in a Plane

Question 1

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

A) 29.1°
B) 13.5°
C) 33.8°
D) 56.2°
E) 60.9°

Answer 1

29.1°

Question 2

A Ferris wheel has diameter of 10 m and makes one revolution in 8.0 seconds. A person weighing 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (that is, the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?

Answer 2

460 N

Question 3

Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station 390 m diameter rotating about its central axis. Astronauts walk on the inside surface of the space station. What rotation period will provide "normal" gravity?

A) 28 s
B) 40 s
C) 6.3 s
D) 4.4 s

Answer 3

28 s

Question 4

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.350. At what speed will the car begin to skid sideways?

A) 9.25 m/s
B) 23.6 m/s
C) 34.3 m/s
D) 35.0 m/s
E) 18.5 m/s

Question 5

Engineers are designing a curved section of a highway. If the radius of curvature of the curve is at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?

A) 23.9°
B) 16.7°
C) 21.0°
D) 26.1°

Question 6

A person on a sled coasts down a hill and then goes over a slight rise with speed 2.7 m/s. The top of this rise can be modeled as a circle of radius 4.1 m. The sled and occupant have a combined mass of 110 kg. If the coefficient of kinetic friction between the snow and the sled is 0.10, what friction force is exerted on the sled by the snow as the sled goes over the top of the rise?

Question 7

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed at which the car can travel around this curve without sliding?

A) 29.6 m/s
B) 33.1 m/s
C) 24.8 m/s
D) 42.0 m/s
E) 37.9 m/s

Question 8

A ball of mass 5.0 kg is suspended by two wires from a horizontal arm that is attached to a vertical shaft, as shown in the figure. The shaft is in uniform rotation about its axis. The rate of rotation is adjusted until the tensions in the two wires are EQUAL. At that speed, the radial acceleration of the ball is closest to

A) 4.9 m/s².
B) 5.9 m/s².
C) 6.9 m/s².
D) 7.9 m/s².
E) 9.9 m/s².

Question 9

A car drives over a hilltop that has a radius of curvature 0.120 km at the top of the hill. At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?

A) 45.5 m/s
B) 41.8 m/s
C) 34.3 m/s
D) 22.2 m/s
E) 27.6 m/s

Question 10

A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.

A) 11.4 m/s
B) 12.5 m/s
C) 10.1 m/s
D) 14.9 m/s

Question 11

Suppose a highway curve is properly banked to eliminate friction for a speed of 45 mph. If your tires were bald and you wanted to avoid sliding on the road, you would have to drive

A) somewhat below 45 mph.
B) somewhat above 45 mph.
C) at exactly 45 mph.

Question 12

If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out because an outward force balances the pull of gravity on the water.

Question 13

The figure shows two wires that are tied to a 710 g mass that revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in the upper wire?

A) 34 N
B) 20 N
C) 27 N
D) 41 N

Question 14

A roadway for stunt drivers is designed for racecars moving at a speed of 40 m/s. A curved section of the roadway is a circular arc of 230 m radius. The roadway is banked so that a vehicle can go around the curve with the friction force from the road equal to zero. At what angle is the roadway banked?

A) 35°
B) 37°
C) 33°
D) 31°
E) 29°

Question 15

The figure shows two wires tied to a 3.3 kg sphere that revolves in a horizontal circle at constant speed. At this particular speed the tension is the SAME in both wires. What is the tension?

A) 24 N
B) 32 N
C) 44 N
D) 22 N

Question 16

A 600-kg car traveling at 24.5 m/s is going around a curve having a radius of 120 m that is banked at an angle of 20°.
(a) Is the curve properly banked for the car's speed?
(b) What is the minimum coefficient of static friction required between the road and the car's tires so the car does not skid?

Question 17

A car travels at a steady 40.0 m/s around a horizontal curve of radius 200 m. What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding?

A) 1.23
B) 0.816
C) 0.736
D) 0.952
E) 0.662

Question 18

A 23 kg mass is connected to a nail on a frictionless table by a massless string 1.3 m long. There is no appreciable friction between the nail and the string. If the tension in the string is 51 N while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution?

A) 4.8 s
B) 3.8 s
C) 4.5 s
D) 5.2 s

Question 19

A 600-kg car traveling at 30.0 m/s is going around a curve having a radius of 120 m that is banked at an angle of 25.0°. The coefficient of static friction between the car's tires and the road is 0.300. What is the magnitude of the force exerted by friction on the car?

A) 1590 N
B) 3430 N
C) 7240 N
D) 7820 N
E) 795 N

Question 20

A string is attached to the rear-view mirror of a car. A ball is hanging at the other end of the string. The car is driving around in a circle, at a constant speed. Which of the following lists gives all of the forces directly acting on the ball?

A) tension and gravity
B) tension
C) tension, gravity, and the centripetal force
D) tension, gravity, the centripetal force, and friction