Momentum Conservation – 100% Correct with Step by Step Calculations

PRACTICE:

1. If a ball is rolling at a velocity of 1.5 m/sec and has a momentum of 10.0 kg·m/sec, what is the mass of the ball?

2. What is the velocity of an object that has a mass of 2.5 kilogram and a momentum of 1,000 kg·m/sec?

3. Tiger Woods hits 45.0-gram golf ball, giving it a speed of 75.0 m/sec. What momentum has Tiger given to the golf ball?

4. A 400-kilogram cannon fires a 10-kilogram cannonball at 20 m/sec. If the cannon is on wheels, at what velocity does it move backward? (This backward motion is called recoil velocity.)

5. “Big” Al stands on a skateboard at rest and throws a 0.5-kilogram rock at a velocity of 10.0 m/sec. “Big” Al moves back at 0.05 m/sec. What is the combined mass of “Big” Al and the skateboard?

6. As the boat in which he is riding approaches a dock at 3.0 m/sec, Jasper stands up in the boat and jumps toward the dock. Jasper applies an average force of 800 Newton’s on the boat for 0.30 seconds as he jumps.

a. How much momentum does Jasper’s 80-kilogram body have as it lands on the dock?

b. What is Jasper’s speed on the dock?

7. Daryl the delivery guy gets out of his pizza delivery truck forgetting to set the parking brake. The 2,000 kilogram truck rolls down hill reaching a speed of 30 m/sec just before hitting a large oak tree. The vehicle stops 0.72 seconds after first making contact with the tree.

a. How much momentum does the truck have just before hitting the tree?

b. What is the average force applied by the tree?

8. Two billion people jump up in the air at the same time with an average velocity of 7.0 m/sec. If the mass of an average person is 60 kilograms and the mass of Earth is 5.98 × 1024 kilograms:

a. What is the total momentum of the two billion people?

b. What is the effect of their action on Earth?

9. Tammy, a lifeguard, spots a swimmer struggling in the surf and jumps from her lifeguard chair to the sand beach. She makes contact with the sand at a speed of 6.00 m/sec leaving an indentation in the sand 0.10 meters deep.

a. If Tammy’s mass is 60 kilograms, what is momentum as she first touches the sand?

b. What is the average force applied on Tammy by the sand beach?

10. When a gun is fired, the shooter describes the sensation of the gun kicking. Explain this in terms of momentum conservation.

11. What does it mean to say that momentum is conserved?

12. What is the momentum of a 100-kilogram fullback carrying a football on a play at a velocity of 3.5 m/sec?

13. What is the momentum of a 75.0-kilogram defensive back chasing the fullback at a velocity of 5.00 m/sec.?

14. A 2,000-kilogram railroad car moving at 5 m/sec to the east collides with a 6,000-kilogram railroad car moving at 3 m/sec to the west. If the cars couple together, what is their velocity after the collision?

15. A 4-kilogram ball moving at 8 m/sec to the right collides with a 1-kilogram ball at rest. After the collision, the 4-kilogram ball moves at 4.8 m/sec to the right. What is the velocity of the 1-kilogram ball?

16. A 0.0010-kg pellet is fired at a speed of 50.0m/s at a motionless 0.35-kg piece of balsa wood. When the pellet hits the wood, it sticks in the wood and they slide off together. With what speed do they slide?

17. Terry, a 70-kilogram tailback, runs through his offensive line at a speed of 7.0 m/sec. Jared, a 100-kilogram linebacker, running in the opposite direction at 6.0m/s, meets Jared head-on and “wraps him up.” What is the result of this tackle?

18. Snowboarding cautiously down a steep slope at a speed of 7.0 m/sec, Sarah, whose mass is 50 kilograms, is afraid she won’t have enough speed to travel up a slight uphill grade ahead of her. She extends her hand as her friend Trevor, having a mass of 100 kilograms is about to pass her traveling at 16 m/sec. If Trevor grabs her hand, calculate the speed at which the friends will be sliding.

19. Tex, an 85.0 kilogram rodeo bull rider is thrown from the bull after a short ride. The 520 kilogram bull chases after Tex at 13.0 m/sec. While running away at 3.00 m/sec, Tex jumps onto the back of the bull to avoid being trampled. How fast does the bull run with Tex aboard?

20. Identical twins Kate and Karen are rowing their boat on a hot Summer afternoon when they decide to go for a swim. Kate, whose mass is 45 kilograms, jumps off the front of the boat at a speed of 3.00 m/sec. Karen jumps off the back at a speed of 4.00 m/sec. If the 70-kilogram rowboat is moving at 1.00m/s when the girls jump, what is the speed of the rowboat after the girls jump?

21. A 0.10-kilogram piece of modeling clay is tossed at a motionless 0.10-kilogram block of wood and sticks. The block slides across a frictionless table at 15 m/sec.

a. At what speed was the clay tossed?

b. The clay is replaced with a “bouncy” ball tossed with the same speed. The bouncy ball rebounds from the wooden block at a speed of 10 meters per second. What effect does this have on the wooden block?

Why?

22. A net force of 100 Newton’s is applied to a 20-kilogram cart that is already moving at 3 meter per second. The final speed of the cart was 8 meters per second. For how long was the force applied?

23. A 3-kilogram ball is accelerated from rest to a speed of 10 m/sec.

a. What is the ball’s change in momentum?

b. What is the impulse?

c. If a constant force of 40 Newton’s is applied to change the momentum in this situation, for how long does the force act?

24. A 2,000-kilogram car uses a braking force of 12,000 Newton’s to stop in 5 seconds.

a. What impulse acts on the car?

b. What is the change in momentum of the car?

c. What is the initial speed of the car?

25. A 60-kilogram high jumper lands on a mat after her jump. The mat brings her to a stop after 1 second. She was traveling at 5.0 m/sec when she landed on the mat. Note: The speed of the jumper at the top of her jump, before she started to fall toward the mat, was 0 m/sec.

a. What is the change in momentum for the jumper?

b. What is the force felt by the jumper upon impact with the mat?

26. A 0.5-kilogram soccer ball is kicked with a force of 50 Newton’s for 0.2 seconds. The ball was at rest before the kick. What is the speed of the soccer ball after the kick?

27. A baseball player hits a 0.155-kilogram fastball traveling at 44.0 m/sec into center field at a speed of 50.0 m/sec. If the impact lasts for 0.00450 second, with what force does he hit the baseball?

28. Tom Sawyer launches his 180-kilogram raft on the Mississippi River by pushing on it with a force of 75 Newton’s. How long must Tom push on the raft to accelerate it to a speed of 2.0 m/sec?

29. In terms of impulse, why is the ride much more comfortable when an airplane is flying at constant speed versus when it is taking off or landing?

30.  The weatherman tells you that today will reach a high of 45°F. Your friend from Sweden asks what the temperature will be in degrees Celsius. What value would you report to your friend?

31.  Your father orders a fancy oven from England. When it arrives, you notice that the temperature dial is calibrated in degrees Celsius. You wish to bake a cake at 350°F. At what temperature will you have to set the dial on this new oven?

32.  Your new German automobile’s engine temperature gauge reads in Celsius, not Fahrenheit. You know that the engine temperature should not rise above about 225°F. What is the corresponding Celsius temperature on your new car’s gauge?

33.  Your grandmother in Ireland sends you her favorite cookie recipe. Her instructions say to bake the cookies at 190.5°C. To what Fahrenheit temperature would you set the oven to bake the cookies?

34.   A scientist wishes to generate a chemical reaction in his laboratory. The temperature values in his laboratory manual are given in degrees Celsius. However, his lab thermometers are calibrated in degrees Fahrenheit. If he needs to heat his reactants to 232°C, what temperature will he need to monitor on his lab thermometers?

35.  You phone a friend who lives in Denmark and tell him that the temperature today only rose as high as 15°F. He replies that you must have enjoyed the warm weather. Explain his answer using your knowledge of the Fahrenheit and Celsius scales and conversion formulas.

36.  A gas has a boiling point of -175°C. At what Kelvin temperature would this gas boil?

37.  A chemist notices some silvery liquid on the floor in her lab. She wonders if someone accidentally broke a mercury thermometer, but did not thoroughly clean up the mess. She decides to find out of the silver stuff is really mercury. From her tests with the substance, she finds out that the melting point for the liquid is 275 K. A reference book says that the melting point for mercury is -38.87°C. Is this substance mercury? Explain your answer and show all relevant calculations.

38.  You are at a Science Camp in Florida. It’s August 1st. Today’s activity is an outdoor science quiz. The first question on the quiz involves a thermometer that reports the current temperature as 90°. You need to state the temperature scale in which this thermometer is calibrated: Kelvin, Fahrenheit, or Celsius. Which scale is correct? Defend your answer with your knowledge of the temperature scales.