Energy and Momentum – In-class Practice (This is not homework!)

1. Determine the kinetic energy of a 1000 kg car traveling at a speed of 10.0 m/s.  Repeat for speeds of 20.0 m/s and 30.0 m/s.  Discuss the significance of the results.

2. A certain cookie has 150 Calories.  1 Calorie (dietetic) is equal to 4190 J of energy.  At what rate of speed would a 1000 kg car have kinetic energy equal to the chemical energy of the cookie?

3. A 500 g mass is placed on a table that is 91.5 cm high.  (a) How much potential energy does the mass have relative to the floor?  (b) How much mass on the same table would have as much energy as the chemical potential energy in a 150 calorie cookie?

4. A 5.0 kg object is launched straight upward with initial speed 30.0 m/s.  (a) Determine its speed when it is 10.0 m above its launch.  (b) Determine the maximum height it will attain.

5. A superball is dropped from a height of 2.00 m.  Measure its mass and its rebound height.  (a) With what speed does the ball hit the floor?  (b) With what speed does the ball leave the floor?  (c) How much kinetic energy does the ball lose during the bounce?

6. A ball of mass 300 g is thrown with initial speed 10.0 m/s toward the ceiling.  The ball hits the ceiling, which is 1.50 m higher than the point of release.  (a) Find the speed of the ball at impact.  (b) Find the kinetic energy at impact.

7. A radical parachutist, mass 90.0 kg, jumps with initial speed 2.00 m/s from atop the St. Louis Arch (height 192 m).  His chute opens at a point 15.0 m below the top of the arch.  (a) Determine the maximum speed that occurs during the stunt.  (b) Should the parachute fail to open, what would be the impact speed?

8. Calculate the maximum speed of a pendulum based on measurements of the minimum and maximum heights as it swings back and forth.  Measure with a CBR and compare.

9. A string is attached to the ceiling and at the other end a ball is attached.  The ball is pulled back to a certain point and released.  At the instant the ball reaches its lowest point the string begins to wind around a horizontal rod placed in its path.  Make appropriate measurements and calculate:  (a) the minimum initial release height that will ensure that the ball completes its first loop around the rod, and (b) the speed of the ball impacting the rod.

10. The engine of a 2500 kg airplane produces thrust 8.50 kN, 180° as the craft accelerates 1500 m, 180° across a level runway.  (a) Determine the work done by the thrust.  (b) Determine the work done by gravity.  (c) Determine the work done by the normal force.

11. The force of friction against a car is 6500 N as the car skids to a stop in 45.0 m.  Find the work done by friction.

12. Wind exerts a force of 2.5 kN, 90° (northward) on the sails of a schooner as it moves 2.0 km, 75° through the water.  Find the work done by the wind.

13. An object of mass 1.50 kg is pushed 2.00 m along a ramp that is inclined 30.0°.  The applied force has magnitude 11.2 N and is directed parallel to the ramp.  Friction has magnitude 3.82 N.  Determine the work done by each force:  the applied force, friction, gravity, and normal force.

14. A parent exerts a force of 80.0 N to push a kid on a tricycle 10.0 m.  Kid & tricycle = 25.0 kg; friction = 35.0 N.  What speed does the kid attain from the push?

15. A car with mass 1400 kg and initial speed 35 m/s brakes and comes to a complete stop in 150 m.  Determine the amount of friction.

16. The engine and transmission of a certain car can do about 16 MJ of work for every gallon of gasoline used.  If friction on this car is 600 N when traveling at constant 25 m/s, what is its fuel economy in km/gallon?  Repeat for a speed of 35 m/s and friction 1000 N.

17. Compare the amounts of work done by the power train:  (a) to accelerate a 1000 kg car from rest to 20 m/s over a distance of 100 m with average friction 190 N,  (b) to move the car 100 m at a constant 20 m/s with friction 380 N.

18. Total friction on a 1993 Ford Festiva can be modeled by three formulas. Rolling resistance: F_R = (0.024) mg. Air resistance: F_A = (0.361 kg/m) v². Engine friction: F_E = (155 N) n, where n = gear ratio. The total mass, including driver, is right at 1000 kg. Assuming the engine is 38% efficient and a gallon of gas has 120.6 MJ of energy, determine the fuel economy in miles per gallon for the following cases: (a) v = 55 mph, n = 0.692 (5^th gear), (b) v = 75 mph, n = 0.692, (c) v = 55 mph, n = 0.861 (4^th gear), and (d) v = 55 mph, n = 0.692, and m = 1400 kg (includes three passengers).

19. Determine the amount of work done by a 100 kg hiker that climbs a mountain along a trail with a change in elevation of 1000 m.

20. A person tosses a 500 g ball into the air.  The person exerts an average force of 60.0 N for a distance of 0.500 m “during the throw”, after which the ball rises straight upward.  Determine the speed of the ball at a point 3.00 m above its release from the person’s hand.

21. How much work must the power train do as a 1500 kg car accelerates from 20.0 m/s to 30.0 m/s along a 200 m stretch of road that rises 10.0 m if there is 700 N of friction?

22. A truck with mass 8000 kg descends a mountain on a road that falls 8.0 m for every 100 m of pavement.  The truck maintains a constant speed.  (a) What amount of friction is there?  (b) How much heat is generated each 1.0 km traveled in this manner?

23. A sled dog exerts a force of 300 N on its harness as it pulls the sled along.  It takes the dog 30.0 minutes to travel a distance of 1.00 km.  Find the dog’s average power output. 

24. A microwave oven is rated at 3.0 kW.  How much energy does it use to cook a hot dog for 1.0 minute?

25. A 60 W light bulb is left on for 1.0 hour.  How much electric energy does it use in this time?  How much time would it take to use 1.0 kWh of energy?

26. A winch is designed for use on a rescue helicopter.  What power electric motor would be required to lift 200 kg at a steady speed of 0.50 m/s?

27. A go-cart and rider, mass 275 kg, is powered by a 3.0 hp engine.  (a) Ignoring friction, what would be the minimum amount of time required to accelerate from rest to 10.0 m/s?  (b) If the actual time required is 12 s, what amount of friction is present?

28. A 6.00 kg bowling ball with speed 9.00 m/s strikes a 750 g pin.  This slows the bowling ball to 7.00 m/s.  Find the speed of the pin due to the impact.

29. Cart A, mass 2.0 kg and velocity 12 m/s, 0°, collides with cart B, mass 7.0 kg at rest.  After the collision, cart B has velocity 4.0 m/s,0°.  Find the velocity of cart A after the collision.

30. A kid uses a pellet gun to fire a 1.0 g pellet into a 15 g can that initially rests atop a fence post.  The pellet is fired with a velocity of 30 m/s, 180°.  Estimate the velocity with which the can flies off the post for the following cases:  (a) The pellet comes to a rest and lands on the post.  (b) The pellet sticks in the can.  (c) The pellet bounces off the can with velocity
5.0 m/s, 0°.  (d) The pellet goes through the can and out the other side with speed 5.0 m/s.

31. A 5.0 kg cannonball is fired with a muzzle velocity 40 m/s, 0° from a cannon that has a mass of 160 kg.  Determine the recoil velocity of the cannon.

32. Two kids on skateboards roll along together (side by side), traveling at 2.00 m/s.  The 60.0 kg kid pulls back on the 50.0 kg kid, which boosts his own speed to 3.00 m/s.  (a) Find the resulting speed of the 50.0 kg kid.  (b) How much momentum is transferred?

33. A boy and a wagon, with total mass 45.0 kg roll with velocity 1.50 m/s, 0.0°.  The boy has with him in the wagon a 0.800 kg brick.  With what velocity would he have to throw the brick in order to stop himself and the wagon?  Give your answer in two different reference frames:  that of the earth and that of the wagon.

34. Let’s revisit the pellet (1.00 g, 30.0 m/s) and the bean can (15.0 g).  For each of the following cases determine the change in kinetic energy of the system:  (a) The pellet comes to rest.  (b) The pellet sticks in the can.  (c) The pellet bounces back off the can at 5.00 m/s.  Which of these cases is most elastic?  Least elastic?

35. Object A, mass 2.00 kg and initial velocity 7.00 m/s, 0.0°, collides with object B, mass 6.00 kg and initial velocity 4.00 m/s, 180.0°.  (a) Determine the greatest amount of kinetic energy that could be “lost” during the collision.  (b) Show that if object B rebounds with velocity 1.50 m/s, 0.0° it would be a perfectly elastic collision.

36. Two objects of the same mass undergo a perfectly elastic collision.  Object A is initially at rest and object B initially has velocity 10.0 m/s, 0°.  Determine the velocity of each object after the collision (assuming the motion is restricted to one dimension).

37. A lab cart with mass 1.5 kg moves with velocity 6.0 m/s, 0° across a track before colliding elastically with a second cart that has a mass of 0.50 kg.  Determine the velocity of each object after the collision.

38. NASA often uses a “gravitational slingshot” to boost the speed of a space probe.  In this maneuver, the probe approaches a planet and swings around it because of the gravity, and then moves away from the planet at a higher speed than it had previously.  This can be analyzed as an elastic “collision”!  Suppose that the planet is Earth (mass 5.974 × 10²⁴ kg, orbital speed = 29.8 km/s) and the space probe has mass 950 kg and initial speed 9.6 km/s.   Determine the boost in speed assuming the probe reverses its direction in the interaction.