Circular Motion Test Review Hons



Circular Motion Test Review Hons : This assignment is due on the day of your test (Friday 02/18). Draw a free body diagram as necessary, for the centripetal force problems.

1. The drawings on the figure below show a mass on the end of a string as it is spun counterclockwise in a vertical circle. Draw the direction of the velocity, acceleration and centripetal force vectors at the points indicated. If the string were cut at each of these four different positions, Sketch the subsequent trajectory of the mass until it lands on the ground.

a. b.

c. d.

2. Which device(s) on a car can be used to control its speed? Which device(s) on a car can be used to control its velocity but not its speed?

3. Draw a free-body diagram for each of the following situations and indicate the force(s) causing Fc for…

a. A car turning a corner on level ground.

b. A model airplane on the end of a string, flying in a horizontal circle.

c. A roller coaster at the top of a vertical loop. (The roller coaster is upside-down.)

d. A car rounding a banked curve.

e. A pendulum released from a 60° angle at the lowest point in its motion.

5. A 500 kg race car rounds a curve with a radius of 100 m.

a. What type of force is the centripetal force in this example?

b. Find the magnitude of the centripetal force acting on the car when it rounds the curve at 20 m/s. (2000 N)

6. Some people rejected the notion that the earth is rotating when it was first proposed. Since the earth is so large, points on the equator would be moving quite fast and it was thought that objects on the equator would be flung off into space. Show that the acceleration due to gravity is more than sufficient to keep this from happening through the following calculations.

a. Find the speed of a point on the equator. (463.9 m/s)

b. Find the centripetal acceleration needed to remain on the equator. (0.033m/s2)

c. How does the acceleration provided by gravity compare to the centripetal acceleration?

(g = 290 ac)

7. A frictionless stunt motorcycle track has a section which is a vertical loop of radius 5.0 m.

a. At what minimum speed should a 100kg motorcycle be driven through the top of the loop? (7m/s)

b. If the force exerted by the track on the motorcycle at the bottom of the loop is 5880N, calculate its speed. (15.65m/s)

8. A 0.10 kg solid rubber ball is attached to the end of an 0.80 m length of light thread. The ball is swung in a vertical circle. The speed of the ball is kept constant at 6.0 m/s throughout this experiment. Determine the tension in the thread at …

a. the top of the circle and (3.52 N)

b. the bottom of the circle.(5.48 N)

9. A rock of mass 2 kg is tied to a string and spun in a vertical circle of radius 10m at a constant speed. At the top of the circle, the tension in the string is twice the weight of the rock. Determine the following quantities.

a. the centripetal force at the top of the circle (58.8 N)

b. the speed of the rock at the top of the circle (17.15 m/s)

c. If the speed of the rock at the bottom of the circle is 23.2m/s, find the tension in the string at the bottom of the circle(127.25 N)

10. As a highway engineer, you wish to design a safe curve for a highway with a speed limit v of 24 m/s (54 mph). Rubber tire on dry pavement has a coefficient of static friction µs of 0.75.

a. Determine the radius of a curve that is just safe enough to allow a car traveling at the speed limit to safely negotiate the curve. .(78.4m)

b. Engineers often "overdesign" their projects to reduce the probability of failure. For example, bridges are built many times stronger than is necessary to just support the weight of traffic. Name at least two things that should be done to ensure that this highway curve is overdesigned.

11. A 653 kg roller coaster car (includes mass of occupants) are passing through a vertical loop. The speed of the car at the top of the loop is 16.9 m/s. What radius of curvature (in meters) must the loop have at its very top in order for the occupants to experience a normal force which is 1/4-th their weight?(23.3 m)

12. A roller coaster vehicle has a mass of 522 kg when fully loaded with passengers (see diagram below).

a. If the vehicle has a speed of 24.9 m/s at point A, what is the g-force of the track on the vehicle at this point? (Given: R1 = 11.1 m; R2 = 16.7 m.)(6.7 g’s)

b. What is the maximum speed (in m/s) the vehicle can have at point B in order that it remain on the track? (12.8 m/s)

13. A 900-kg car makes a 180-degree circular turn with a speed of 10.0 m/s. The radius of the circle through which the car is turning is 25.0 m. Determine the force of friction and the coefficient of friction acting upon the car.(3600 N, 0.408)

14. The swings at an amusement park revolve so that the outside swing has a linear speed of 4.5 m/s. At that

speed, the outside swing travels a circle of radius 8 meters.

a. What angle does the swing make with the vertical at this speed?(14.50)

b. If a rider has a mass of 45 kg, what is the tension in the cable holding the swing?(455.5N)

15. Determine earth’s acceleration due to gravity at the location of, as well as the orbital period, and the orbital velocity, of an object orbiting the Earth 3.38X107 m above the Earth’s surface. ( 0.349 m/s2, 61822.2s, 3435.2m/s )

16. How far above the Earth’s surface would you have to go for your weight to be reduced to one-sixth of what it is on the Earth’s surface? (9.25X106m )

17. Two masses m1 and m2, are separated by a distance r. The force of attraction between the two masses is 20N.

a. If m1 is doubled, how does F change? ____________________

b. If neither of the masses were changed, but r was doubled, how would F change?____________________

c. If r was not changed but both masses were doubled, how would F change?____________________

d. If r was halved and both masses were doubled, how would F change?____________________

18. Where would a rock weigh less, on the top of Mount Everest, or at the lowest point of Death Valley? Explain your answer.

19. Determine the minimum angle at which a road should be banked so that a car traveling at 20.0 m/s can safely negotiate the curve if the radius of the curve is 200.0 m. (11.50)

20. A stopper tied to the end of a string is swung in a horizontal circle.  If the mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8 s,

a.  what is the tension in the string?( 0.34 N)

b.  what would happen to the tension on the string if the mass was doubled and all other quantities stayed the same?

c.  what would happen to the tension on the string if the period was doubled and all other quantities stayed the same?

21. Determine the centripetal acceleration (in m/s2) of a rider on the Cajun Cliffhanger (a barrel ride at an amusement park) if the rider makes 7.4 revolutions around the 6.53-m diameter circle in 26.1 seconds. What is the time period of the rider? (20.7 m/s2, 3.52s)

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