General Physics - University Physics



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University Physics I

PHYS 2325

Fall 2013

Exam 4 Practice Problems

This collection of problems is only meant as practice. If a particular topic isn’t covered by these problems, it should not be taken as a guarantee that it won’t appear on the exam.

1. A 30.0 kg child rides a Ferris wheel that has a radius of 20.0 m. It takes 15.0 s to make one full revolution. Calculate the normal force of the seat upward on the child when she is at (a) the top and (b) the bottom of the Ferris wheel. (Answers: 190 N, 400 N)

2. Planet A and planet B both follow circular orbits around the same star. Planet B has twice the mass of planet A, and is 10 times farther away from the star. How many times longer is a year on planet B than a year on planet A? (Answer: 31.6 times longer)

3. A 1000 kg roller coaster car crosses the top of a loop of radius 10.0 m at a speed of 20.0 m/s. Calculate the normal force of the track on the coaster. (Answer: 30200 N)

4. A puck of mass 1.50 kg slides in a circle of radius r = 20.0 cm on a frictionless table while attached to a hanging cylinder of mass 2.50 kg by a cord through a hole in the table, as shown in the figure below. The cylinder remains at rest. How much time does it take for the puck to make one complete revolution around the circle? (Answer: 0.69 s)

[pic]

5. A wrecking ball has a mass of 75 kg and swings from a cable that is 5.2 m long. If it is moving at a speed of 19 m/s at the bottom of the swing, when the cable is vertical, what is the tension in the cable at that moment? (Answer: 5940 N)

[pic]

6. A tiny, lead sinker with a mass of 30.0 g swings in a horizontal circle at the end of a length of thread at a rate of 1.50 revolutions per second. The radius of the circle is 10.0 cm. Calculate the angle that the string makes with the vertical. (Answer: 42.2 degrees)

7. Cart A, with a mass of 2.00 kg, coasts rightward at an initial speed of 1.25 m/s on a level, frictionless track. It collides with cart B, which has a mass of 3.00 kg and is initially coasting leftward at a speed of 0.800 m/s. After the collision, B is coasting rightward at a final speed of 0.200 m/s.

a) Calculate the final speed of A. (Answer: 0.25 m/s)

b) Is cart A moving leftward or rightward after the collision? (Answer: leftward)

8. Identical pucks slide down a frictionless incline. Puck B starts sliding from an initial height that is twice as high as puck A’s initial height. By what factor is puck B’s final speed at the bottom of the incline greater than puck A’s? Explain carefully how you know.

9. Two springs are compressed through the same distance. Spring B has a spring constant that is three times as large as spring A’s spring constant. By what factor is the elastic potential energy of spring B greater than the elastic potential energy of spring B? Explain carefully how you know.

10. Two identical pucks are launched across a surface that exerts identical friction forces on each. In order to make puck B slide 3 times as far across the surface as puck A, by what factor must puck B’s initial speed be greater? Explain carefully how you know.

11. A tiny metal ball is suspended at the end of a 16.0 cm thread. The ball is pulled 60.0 degrees away from its equilibrium position and released from rest with the thread taut, as shown below. Calculate the speed at which it swings through the bottom of its arc. (Answer: 1.25 m/s)

[pic]

12. A bizarre (and lethal) new amusement park ride involves a roller coaster car of total mass 1500 kg (including passengers) that is launched from rest along a level, frictionless track by an anchored, horizontal spring of spring constant k = 115000 N/m initially compressed through a distance of 3.00 m. Calculate the speed of the car at the top of the first hill, which is 20.0 m high. (Answer: 17.3 m/s)

[pic]

13. A 0.89 kg puck, initially coasting at 6.2 m/s over level, frictionless ice is acted on by a force, opposite its direction of motion, which slows it down to 3.2 m/s. Calculate the magnitude of the impulse imparted to the puck by this force. (Answer: 2.67 kg·m/s)

14. Dynamics cart A, having a mass of 250 g and coasting to the right at an initial speed of 1.50 m/s on a level, frictionless track, collides with cart B, having a mass of 430 g and initially sitting at rest. After the collision, cart A bounces back and coasts to the left at a speed of 0.318 m/s. What is the final speed of B? (Answer: 1.06 m/s)

15. Two stones are launched upward from the ground. Stone B reaches a maximum height that is twice as high as stone A’s maximum height. By what factor was stone B’s launch speed greater than stone A’s launch speed? (Answer: [pic])

16. Two dynamics carts travel along a level, frictionless track. Cart B has twice the mass of cart A and is traveling 3 times as fast. By what factor is cart B’s momentum greater than that of cart A? (Answer: 6)

17. For the situation in problem 16, by what factor is cart B’s kinetic energy greater than cart A’s? (Answer: 18)

18. Two identical pucks are launched by horizontal springs across a level, frictionless surface. After sliding away from the spring, they climb up a frictionless incline. Spring B has twice the spring constant of spring A, but both springs are compressed through the same distance before the launch. By what factor is puck B’s final height on the incline greater than puck A’s final height? (Answer: 2)

19. The two pucks in problem 18 are launched again. However, this time, spring B has the same spring constant as spring A, but is compressed only half as far. By what factor is puck B’s final height on the incline lower than puck A’s final height? (Answer: ¼, i.e., puck B climbs only one-fourth as high as puck A.)

20. Stone B has just as much gravitational potential energy as stone A, but is twice as high above y = 0. By what factor is stone B’s mass less than stone A’s mass? (Answer: ½, i.e., stone B has only one half the mass of stone A.)

21. A 1500-kg car traveling at 12.0 m/s is rammed from behind by a 2200 kg truck traveling in the same direction. No brakes are ever applied, and the two vehicles lock together upon collision and move together at 19.0 m/s. Calculate the initial speed of the truck. (Answer: 24.0 m/s)

22. Frosty the Snowman lies belly down on top of a 10.0 m high hill, initially at rest, and slides all the way down to the bottom, onto a level plain. What is his final speed? (Answer: 14.0 m/s)

23. A 10.0 g dart is fired horizontally out of a dart gun by a spring of spring constant 100 N/m that is initially compressed through a distance of 10.0 cm. Assuming that the barrel of the gun is frictionless, calculate the launch speed of the dart. (Answer: 10.0 m/s)

24. A car that is coasting on a level stretch of road at an initial speed of 22.0 m/s encounters a hill that rises up to a new level stretch of road, 6.20 m higher than the first. Assuming that it continues coasting and that friction and air drag are negligible, calculate the final speed of the car. (Answer: 19.0 m/s)

25. A dynamics cart coasts through two photogates, 0.870 m apart, attached to a straight track inclined at 0.320 degrees above the horizontal. As it coasts down the incline through the first gate, its speed is measured to be 0.343 m/s. What speed is measured as it coasts through the second gate? (Answer: 0.461 m/s)

26. A 1.25 kg dynamics cart is launched from rest by an anchored horizontal spring that has a spring constant of 115 N/m and is initially compressed through a distance of 10.0 cm. It travels on a frictionless track until slowing to a stop at the top of a round hill. Calculate the height of the hill. (Answer: 4.69 cm)

27. (HR8.27) An 8.00 kg sphere is pushed down onto a vertical spring of spring constant 784 N/m, so that the spring is compressed through a distance of 40.0 cm, as shown in the figure below. The sphere is then released from rest, so that the spring launches it upward into the air. Calculate the maximum height that it rises above the point of release. (Answer: 80.0 cm)

[pic]

28. (Knightcalc 10.67) A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 50.0 cm below the ceiling. If a 100 g clay ball is placed gently on the pan, the pan hangs 60.0 cm below the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan. What is the pan’s distance from the ceiling when the spring reaches its maximum length? (Answer: 0.93 m)

29. Car A, having a mass of 2500 kg and traveling due south at an initial speed of 15 m/s, collides with car B, having a mass of 2100 kg and traveling in a direction 30 degrees east of due north. They stick together after the collision and move due east. What was the initial speed of B? (Answer: 20.6 m/s)

30. A titanium sphere of mass m rolls due east on a pool table with an initial speed of 70.0 cm/s toward a steel sphere of mass 1.50m that is rolling due west at an initial speed of 90.0 cm/s. They have a head-on, elastic collision. Calculate the final speeds and directions of (a) the titanium sphere and (b) the steel sphere. (Answers: 1.22 m/s due west, 0.38 m/s due east)

31. Two blobs of clay slide on a level, frictionless surface in the x-y plane. Blob A, with mass 0.200 kg, slides at 30.0 m/s along the x-axis in the positive direction. Blob B, with mass 0.800 kg, slides at 10.0 m/s along the y-axis in the positive direction. They collide at the origin and stick together. (a) Calculate the final speed of the resulting blob. (b) Calculate the direction of motion of the final blob as an angle east of due north. (Answers: 10.0 m/s, 36.9 degrees)

32. Two blocks of clay slide on a level, frictionless plane. Block A, having a mass of 1.50 kg and traveling due south at 10.0 m/s, collides with block B, having a mass of 2.50 kg and traveling 30.0 degrees west of due north at 30.0 m/s. They stick together after the collision. (a) Calculate the final speed of the resulting blob. (b) Calculate the direction of motion of the final blob as an angle west of due north. (Answers: 15.6 m/s, 36.9 degrees)

33. Two blocks of clay slide over a level, frictionless plane. Block A has a mass of 5.00 kg and slides due east at an initial speed of 10.0 m/s. Block B has a mass of 1.5 kg and slides in a direction 30.0 degrees west of due north at an initial speed of 20.0 m/s. They collide and stick together. (a) Calculate the final speed of the resulting blob. (b) Calculate the direction of motion of the final blob as an angle north of due east. (Answers: 6.70 m/s, 36.6 degrees)

34. A 175 kg wrecking ball with its center of mass 20.0 m from the suspension point is pulled 60.0 degrees from the vertical, as shown in the diagram below, so that it is raised a distance of 10.0 m above its equilibrium position. It is then released from rest. Calculate the tension in the cable at the bottom of its swing. (Answer: 3430 N)

[pic]

35. A 1000-kg car coasting at initial speed 30.0 m/s on a level stretch of road encounters a hill of height 25.0 m whose rounded top has radius of curvature 100.0 m. Calculate the normal force of the road on the car at the top of the hill. (Answer: 6000 N)

36. A ballistic pendulum can be used to measure the speed of a bullet. A 5.40 kg block of wood hangs initially at rest from a massless cord. The distance between the support point of the cord and the center of the block is 12.6 cm. A bullet of mass 9.50 g is fired from a gun directly into the block and imbeds itself. The block then swings a maximum angle of 60.0 degrees away from the vertical. What is the muzzle speed of the gun? (Answer: 630 m/s)

37. (HR8.25) Batman weighs 688 N and swings from the roof of a building on an 18 m long batrope from an initial angular displacement of 34.7 degrees from the vertical. What is the maximum tension in the batrope during the swing? (Answer: 930 m/s)

38. The graph below gives the potential energy as a function of position for a particle of mass 10.0 g that is released from rest at x = 3.00 m.

a) What kinetic energy will it have when it reaches x = 4.00 m? (Answer: 2.00 J)

b) What speed will it have when it reaches x = 4.00 m? (Answer: 20.0 m/s)

c) How far will it travel to the right before reversing direction? (Answer: 4.00 m)

d) What will be its maximum speed during its motion from x = 3.00 m to the turning point? (Answer: 28.3 m/s)

e) With what minimum initial kinetic energy must it be projected leftward from x = 3.00 m in order to reach x = 1.00 m? (Answer: 2.00 J)

f) With what minimum initial speed must it be projected leftward from x = 3.00 m in order to reach x = 1.00 m? (Answer: 20.0 m/s)

g) Are there any stable equilibria? If so, where?

h) Are there any unstable equilibria? If so, where?

39. A particle of mass 2.00 kg travels along the x-axis in the negative direction at a speed of 2.00 m/s at t = -3.00 s. Force Fx = (8.00t + t2) N is exerted on the particle between

t = -3.00 s and t = 1.50 s. What is the particle’s velocity at t = 1.50 s? (Answer: -10.4 m/s)

40. HR6.87. A block with a mass of 5.00 kg is pushed through a distance of 2.00 m across the ceiling by a force P of magnitude 80.0 N, acting at an angle of 70.0 degrees above the horizontal. The coefficient of kinetic friction between the block and the ceiling is 0.400. Calculate (a) the (pseudo)work done on the block by friction, (b) the work done by gravity, (c) the work done by the normal force, (d) the work done by P, and (e) the final speed of the block, assuming that it is initially at rest, using the work-kinetic energy theorem. (Answers: -20.9 J, 0 J, 0 J, 54.7 J, 3.68 m/s)

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19 m/s

60º

60°

100 m

U (J)

0

4

8

12

x (m)

2

4

6

8

0

P

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