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Object Acceleration and Gravitational Forces

Explore the ways objects can be accelerated and the forces of attraction between masses. Understand centripetal acceleration and gravitational force equations.

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Object Acceleration and Gravitational Forces

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  1. Chapter 7 Review

  2. 1. In what three ways can an object be accelerated?

  3. Speed up, slow down, change direction.

  4. 2. What is the direction of centripetal acceleration?

  5. Toward the center of the curve or circle.

  6. 3. A girl swings on a swing set at a linear speed of 3 m/s. If her center of mass is 2.5 meters from the point where her swing is attached, what is her centripetal acceleration?

  7. aC = v2/r aC = 32/2.5 aC = 3.6 m/s2

  8. 4. A boy goes through the motion of throwing a baseball. If his arm is one meter long, and the speed of the ball through the arc of the throw is 15 m/s, what is the centripetal acceleration of the ball?

  9. aC = v2/r aC = 152/1 aC = 225 m/s2

  10. 5. What is the direction of centripetal force?

  11. Toward the center of the curve or circle.

  12. 6. The Spinnaker ride at Six Flags was a spinning cylinder that pressed its riders against the inside of the cylinder while the floor dropped out beneath them. If the cylinder is 10 meters across and it spins at 28 revolutions per minute: A) What is the centripetal acceleration? Express this in terms of g.

  13. 28 rev/min x 10p x 1 min/60 s= 14.65 m/saC = v2/r aC = 14.652/5 aC = 43 m/s243 m/s2 / 10 m/s2 = 4.3 g’s

  14. B) What force is applied to a 70 kg rider?

  15. F = maF = 70 x 43 m/s2F = 3010 N

  16. C) What minimum frictional force must be applied to the 70 kg rider to keep them from sliding down the wall?

  17. Friction must be equal to the weight.Wt = mgWt = 70 x 10Wt = 700 N

  18. D) If this minimum force is applied, what is the coefficient of friction between the rider and the wall?

  19. m = f / FNm = 700 / 3010m = 0.233

  20. 7. Two masses are 20 cm apart and have a gravitational attraction of 20 N. A) If they are moved to a distance of 40 cm apart, what is the force between them?

  21. By F = Gm1m2/d2, if d doubles (20 cm to 40 cm), F must decrease by a factor of 4.20/4 = 5 N

  22. B) What is the force if they are moved to a distance of 10 cm apart?

  23. By F = Gm1m2/d2, if d is halved (20 cm to 10 cm), F must increase by a factor of 4.20 x 4 = 80 N

  24. 8. Two loaded trucks have masses of 25,000 kg and 27,000 kg. If their centers of gravity are 10 meters apart, what is the force between them?

  25. F = Gm1m2/d2F = 6.67 x 10-11 x25000 x 27000/102F = 4.5 x 10-4 N

  26. 9. What is the force of attraction between the moon and the earth at their maximum separation distance of 405,000,000 meters? The mass of the earth is 6 x 1024 kg. The mass of the moon is 7.4 x 1022 kg.

  27. F = Gm1m2/d2F = (6.67 x 10-11)(6 x 1024) (7.4 x 1022)/(4.05 x 108)2F = 1.81 x 1020 N

  28. 10. What is the force of attraction between the moon and the earth at their minimum separation distance of 363,000,000 meters?

  29. F = Gm1m2/d2F = (6.67 x 10-11)(6 x 1024) (7.4 x 1022)/(3.63 x 108)2F = 2.25 x 1020 N

  30. 11. What is the force of attraction between the earth and Pluto? Pluto’s mass is 1.3 x 1022 kg and its average distance from earth is 5.91 billion km.

  31. F = Gm1m2/d2F = (6.67 x 10-11)(6 x 1024) (1.3 x 1022)/(5.91 x 1012)2F = 1.49 x 1011 N

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