PHY1 Review for Exam 5

Transcription

1 Topics 1. Uniform circular Motion a. Centripetal acceleration b. Centripetal force c. Horizontal motion d. ertical motion e. Circular motion with an angle 2. Universal gravitation a. Gravitational force b. Kepler s law Earth-sun distance = 1.49 x 10 8 km Earth moon distance = 3.84 x 10 5 km Equations = 2πr / T a c = 2 /r F = ma F = Gm 1 m 2 /r 2 (T 1 /T 2 ) 2 = (r 1 /r 2 ) 3 F F = µf N Constants G = 6.67 x N m 2 /kg 2 Earth: Mass = 5.97 x kg Radius = 6.38 x 10 3 km Moon Mass = 7.35 x kg Radius = 1.74 x 10 3 km Sun Mass = 1.99 x kg Radius = 6.96 x 10 5 km Multiple Choice Questions 1. A ball attached to a string is moved at constant speed in a horizontal circular path. A target is located near the path of the ball as shown in the diagram 3. The diagram below represents two satellites of equal mass, A and B, in circular orbits around a planet. At which point along the ball s path should the string be released, if the ball is to hit the target? (1) A (3) C (2) B (4) D 2. As an astronaut travels from the surface of the earth to a position that is four times as far away from the center of the earth, the astronaut s (1) mass decreases. (2) mass remains the same. (3) weight increases (4) weight remains the same. Compared to the magnitude of the gravitational force of attraction between satellite A and the planet, the magnitude of the gravitational force of attraction between satellite B and the planet is (1) half as great. (2) twice as great. (3) one-fourth as great. (4) four times as great.

2 4. The diagram below shows a 5.0 kilogram bucket of water being swung in a horizontal circle of 0.70 meter radius at a constant speed of 2.0 meters per second. 6. In the diagram below, S is a point on a car tire rotating at a constant rate. Which of the following graphs best represent the magnitude of the centripetal acceleration of point S as a function of time during one complete revolution of the tire? The magnitude of the centripetal force on the bucket of water is approximately (1) 5.7 N (3) 29 N (2) 14 N (4) 200 N 5. In the diagram below, a cart travels clockwise at constant speed in a horizontal circle. Base your answers to questions 7 thru 9 on the information and diagram below. At the position shown in the diagram, which arrow indicates the direction of the centripetal acceleration of the cart? The diagram shows the top view of a 65 kilogram student at point A on an amusement park ride. The ride spins the student in a horizontal circle with a radius of 2.5 meters, at a constant speed of 8.6 meters per second. The floor is lowered and the student remains against the wall without falling to the floor. (1) A (3) C (2) B (4) D

3 9. The magnitude of the coefficient of friction between the students back and the surface of the ride can not be less than (1) 0.33 (3) 9.8 (2) 30 (4) Which vector best represents the centripetal acceleration of the student at point A? 8. The magnitude of the centripetal force acting on the student at point A is approximately (1) 1.2 x 10 4 N (3) 2.2 x 10 2 N (2) 1.9 x 10 3 N (4) 3.0 x 10 1 N 10. A ball of mass M at the end of a string is swung in a vertical circular path with constant speed (), as shown in the diagram below. At what point is the string most likely to break because it has the greatest tension? D A C (1) A (3) C (2) B (4) D B 11. A 1.0 x 10 3 kilogram car travels at a constant speed of 20 meters per second around a horizontal circular track. Which diagram correctly represents the direction of the car s velocity (v) and the direction of the centripetal force (F c ) acting on the car at one particular moment?

4 Short Answer Questions (Show all work) 12. A child on a merry-go-round is moving with a speed of 1.35 m/s when 1.20 m from the center of the merry-go-round. Calculate (a) the centripetal acceleration of the child, and (b) the net horizontal force exerted on the child whose mass is 25.0 kg. (c) What happens to the speed when the child moves towards the center of the merry-go round assuming that the period of revolution remains the same? 13. A 0.40 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 exceeds 60 N, what is the maximum speed the ball can have? 14. At what speed must a roller coaster be traveling when upside down at the top of a circle if the passengers who are not wearing their seat belts don t fall out. Assume a radius of curvature of 8.6 m.

5 15. Using Newton s law of universal gravitation determine the force of gravity between the earth and the moon. 16. By combining Newton s universal law of gravitation and F = m 2 /r, calculate the velocity of a satellite moving in a stable orbit about the earth at a height of 3600 km. 17. Qualitatively describe the orbit of Halley s comet around the sun based on your understanding of the elliptical orbit and the corresponding force and velocity vectors at various positions in the orbit. Draw a picture of the orbit with vectors to support your discussion.

6 Answers (a) 1.52 m/s 2 ; (b) 38.0 N; (c) Since the radius decrease the speed also decreases, assuming that the period of revolution remains the same m/s m/s x N x 10 4 m/s, m 1 cancels and be sure to use the mass of the earth as m The force of gravity is greatest when the comet is closest to th sun and the velocity is also the greatest. The velocity vector is perpendicular to the force vector which is pointed at the sun. The velocity and force vectors are also perpendicular at the furtherest point from the sun, where they are the smallest. At position where the comet is moving away from the sun the angle between the velocity and force vectors is gretaer than 90. The force vector is always pointed at the sun and the velocity vector is tangential to the orbit. When the comet is moving towards the sun the angle between the force and velocity vectors is less than 90.