By
Valentina Tobos | Laurentiu Tobos Updated on Sep 26, 2011
Review these concepts at: Linear Momentum Study Guide
Practice Questions
- Does a larger mass necessarily mean a larger momentum? Explain briefly.
- In what conditions can an object have zero momentum? Explain briefly.
- Can an object have negative momentum? Explain briefly.
- What is the connection between the unit for impulse and for momentum?
- Are impulse and force measuring the same quantity? Explain briefly.
- Does a large force always produce a large impulse? Explain briefly.
- Consider the time dependence for a force such as the one in Figure 6.2. Based on the data given, estimate the impulse.
- If you are to receive a hit from a ball, would you rather make it last a longer or a shorter time?
- Why do some brittle objects break when they hit a hard floor but survive a fall on a carpeted floor? Explain briefly.
- Is it correct to say that momentum and impulse measure the same quantity? Explain briefly.
- In which case is the impulse greater: when an object slows down to half of the speed or when it stops completely? Explain briefly.
- Is it possible for an object to move and have zero impulse? Explain briefly.
- A car comes to a complete stop in 15 seconds. Consider the mass of the car to be 1,500 kg and the initial speed to be 18 m/s. Find the average breaking force.
- What difference in the conservation of momentum does it make that the momentum is a vector quantity? Explain briefly.
- Can you have three objects moving and have the total momentum of the three-body system zero? Explain briefly.
- In the previous example with the rollerblades, how can you start moving without stepping down (remember, you are holding the ball in your arms)? Explain briefly.
- Would it help more if the ball was a medicinal ball, say of mass 10 kg, rather than a soccer ball that you can throw at the same speed? Why or why not?
- A ball suffers a horizontal collision with a (non-moving) wall. Are the vector interpretations of momentum and impulse important in this case? Why or why not?
- Two identical objects, 1 and 2, headed in the same direction collide perfectly elastically. After the collision, object 1 comes to a rest. Compare the velocity of object 2 after the collision with that of object 1 before the collision (is it equal, larger, smaller?).
- Two equal-mass atomic particles move in the same direction with speed v_{1} and v_{2}. One catches up with the second, and they collide perfectly inelastically. What is the speed of the system after the collision compared to before the collision as a function of v_{1} and v_{2}?
- A small piece of clay is thrown at a moving bike, and the clay sticks to the bike. What happens to the speed of the bike if the mass of the clay is much smaller than the mass of the bike?
- A firecracker set on the ground splits into two pieces of equal sizes that spread in two opposite directions. How do the speeds of the two pieces compare?
- In practice problem 22, how do the velocities compare? Why?
- Two cars approaching from different directions (say east and north) collide. Is it possible for the momentum to be zero immediately after collision? Explain.
- What if the cars in practice problem 24 collide head on? Is it possible for the momentum to be zero immediately after the collision? Explain.
- Consider again the firecracker in practice problem 22, but in this case moving upward in the NW direction with a speed of 15 m/s. If the mass of the firecracker is 800 g and it splits in three pieces of mass m_{3} = 2 · m_{2} = 10 · m_{1} with the second piece flying after collision in the west direction at 10 m/s, and the third piece flying north at 12 m/s, find the x and y component of the velocity for the first piece.
- Write each velocity in practice problem 26 as a vector quantity. Use both the component form with (a_{x},a_{y}) and the value + angle form.
- What is the mass of each of the three pieces in practice problem 24?
Answers
- No, speed could be zero or very small.
- Only when speed is zero, because there can be no zero moving mass.
- Yes, if the velocity is in the negative direction.
- They are the same.
- No, since impulse also considers the time of interaction.
- No, the time of interaction can be negligible and then the impulse tends to zero.
- 225 N · s
- Longer since the force then would be smaller.
- Because on the carpet, the time of interaction is longer and the force of impact is smaller.
- No, momentum is a quantity of state, while impulse measures a state change.
- When the object stops
- If the object moves at a constant speed, there is no change in momentum, so no impulse.
- F = 1,800 N
- The momentum being constant means that when we consider momentum a vector both the magnitude and the direction of the momentum have to be the same in the initial and final states.
- Since momentum is a vector, you can have the following situation:
- Throw the ball in a horizontal direction.
- Yes, it would have more momentum.
- Yes. Because speed changes direction before and after collision and velocity, momentum and impulse will consider direction also.
- v_{2 after collision} > v_{2 before collision}
- v_{f} = (v_{1} + v_{2})/2
- The speed of the bike will almost be unchanged and at most decrease by a small amount.
- Equal and opposite, because the final momentum has to be equal to the initial momentum, which was zero.
- Equal in magnitude, opposite in direction.
- No, the resultant immediately after collision is nonzero.
- Yes, if the momenta of the two cars are equal and opposite.
- v_{1x} = 120 m/s and v_{1y} = 50 m/s
- Before explosion: ( –10.6; 10.6) m/s or 15 m/s at 135° with respect to the x-axis
After collision, the first piece moves at (120; 50) m/s or 130 m/s at 23° with respect to the x-axis. The second moves at (–10; 0) m/s or 10 m/s at 1800 with respect to the x-axis, and the third piece moves at (0; 12) m/s or 12 m/s at 90° with respect to the x-axis.
- 0.05 kg, 0.25 kg, and 0.5 kg
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