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Under what circumstances is momentum conserved?
Momentum is conserved when the mass of the system of interest remains constant during the interaction in question and when no net external force acts on the system during the interaction.
Can momentum be conserved for a system if there are external forces acting on the system? If so, under what conditions? If not, why not?
Explain in terms of momentum and Newton’s laws how a car’s air resistance is due in part to the fact that it pushes air in its direction of motion.
To accelerate air molecules in the direction of motion of the car, the car must exert a force on these molecules by Newton’s second law $\overrightarrow{F}=d\overrightarrow{p}\text{/}dt$ . By Newton’s third law, the air molecules exert a force of equal magnitude but in the opposite direction on the car. This force acts in the direction opposite the motion of the car and constitutes the force due to air resistance.
Can objects in a system have momentum while the momentum of the system is zero? Explain your answer.
A sprinter accelerates out of the starting blocks. Can you consider him as a closed system? Explain.
No, he is not a closed system because a net nonzero external force acts on him in the form of the starting blocks pushing on his feet.
A rocket in deep space (zero gravity) accelerates by firing hot gas out of its thrusters. Does the rocket constitute a closed system? Explain.
Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of $1.50\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{kg}$ and a velocity of $(0.30\phantom{\rule{0.2em}{0ex}}\text{m/s})\widehat{i}$ , and the second having a mass of $1.10\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{kg}$ and a velocity of $\text{\u2212}(0.12\phantom{\rule{0.2em}{0ex}}\text{m/s})\widehat{i}$ . What is their final velocity?
$(0.122\phantom{\rule{0.2em}{0ex}}\text{m/s})\widehat{i}$
Two identical pucks collide elastically on an air hockey table. Puck 1 was originally at rest; puck 2 has an incoming speed of 6.00 m/s and scatters at an angle of $30\text{\xb0}$ with respect to its incoming direction. What is the velocity (magnitude and direction) of puck 1 after the collision?
The figure below shows a bullet of mass 200 g traveling horizontally towards the east with speed 400 m/s, which strikes a block of mass 1.5 kg that is initially at rest on a frictionless table.
After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit.
a. 47 m/s in the bullet to block direction; b. $70.6\phantom{\rule{0.2em}{0ex}}\text{N}\xb7\text{s}$ , toward the bullet; c. $70.6\phantom{\rule{0.2em}{0ex}}\text{N}\xb7\text{s}$ , toward the block; d. magnitude is $2.35\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{N}$
A 20-kg child is coasting at 3.3 m/s over flat ground in a 4.0-kg wagon. The child drops a 1.0-kg ball out the back of the wagon. What is the final speed of the child and wagon?
A 5000-kg paving truck coasts over a road at 2.5 m/s and quickly dumps 1000 kg of gravel on the road. What is the speed of the truck after dumping the gravel?
3.1 m/s
Explain why a cannon recoils when it fires a shell.
Two figure skaters are coasting in the same direction, with the leading skater moving at 5.5 m/s and the trailing skating moving at 6.2 m/s. When the trailing skater catches up with the leading skater, he picks her up without applying any horizontal forces on his skates. If the trailing skater is 50% heavier than the 50-kg leading skater, what is their speed after he picks her up?
5.9 m/s
A 2000-kg railway freight car coasts at 4.4 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 3.0 m/s, what is the maximum mass of grain that it can accept?
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