
Newton’s third law states that any two interacting objects push or pull each other with equal (and opposite) force. One key consequence of Newton’s third law is that the total momentum of any closed system is conserved (does not change). If two objects push each other away, their individual momenta change by equal amounts, though in opposite directions, resulting in a zero net change in the momentum of the system. Conservation of momentum forms the basis for understanding rocketry, jet propulsion, and the recoil motions of guns and cannons.

law of conservation of momentum

Review problems and questions 


The law of conservation of momentum applies to closed systems. What does the term “closed system” mean in this context?
 No force of any kind can act upon any object within the system.
 No net force can act upon any object within the system.
 No net force may operate upon the system from outside the system.

The correct answer is c. In the context of momentum conservation, we are concerned with external forces. The objects within a system may experience external forces such as gravity (weight) and may accelerate due to a net force from another object within the system. However, momentum is only conserved within a system of objects when the net external force on that system is zero. A closed system is one in which there is no net external force. (As an example, this can occur if the interacting objects are all on a level surface such as a floor or countertop. In that case, each object’s weight is cancelled out by a normal force.)


Jaime and Ayesha stand motionless while wearing roller skates. They gently press on each others’ hands, palms up. Each friend then rolls away at a speed of 0.8 m/s. Which statement accurately compares their masses?
 Jaime and Ayesha have equal masses.
 Jaime is more massive than Ayesha.
 Jaime is less massive than Ayesha.
 There is not enough information to compare their masses.

The correct answer is a: Jaime and Ayesha have equal masses. How do we know? According to the law of conservation of momentum, Jaime and Ayesha gain equal amounts of momentum when they push each other. Since they were motionless to start with, this gained momentum is all each of them has. Momentum equals mass times velocity (p = mv). Jaime and Ayesha have equal p values and equal values for v; therefore, they must also have equal masses (m).


During a spacewalk, Dmitri finds himself floating 3 m from his space station’s airlock. He only has one minute of air left. He has one detachable 10 kg toolkit, which he can toss to propel himself toward safety.
 How fast will he need to move to reach the airlock before he runs out of air?
 Dmitri and his space suit together have a mass of 100 kg. How fast must he throw the toolkit to propel himself toward the airlock at the required speed (found in the previous step)?

Answer:  To save himself, Dmitri must move toward the airlock at a speed v of at least 0.05 m/s (5 cm/s).
 Dmitry has to eject the toolkit at a speed of 0.5 m/s, or 50 cm/s.
Solution: Asked: recoil speed v of Dmitri
Givens: distance d = 3 m, time interval Δt = 60 s Relationship: v = d /Δt Solve:$$v=\frac{3\text{m}}{60\text{s}}=0.05\text{m/s}=5\times {10}^{2}\text{m/s}$$Answer: To save himself, Dmitri must move toward the airlock at a speed v of at least 0.05 m/s (5 cm/s).  Asked: speed v_{tk} of the toolkit
Givens: Dmitri’s speed v_{D} = 0.05 m/s and mass m_{D} = 100 kg; toolkit’s mass m_{tk} = 10 kg Relationship: $${m}_{1}{v}_{i1}+{m}_{2}{v}_{i2}={m}_{1}{v}_{f1}+{m}_{2}{v}_{f2}$$Solve: First, let Object 1 be Dmitry and Object 2 be the toolkit. Next, let the positive direction be toward the airlock (i.e., v_{D} > 0 and v_{tk} < 0). The initial velocities are both zero. The formula therefore becomes$$0={m}_{D}{v}_{D}+{m}_{tk}{v}_{tk}$$By inserting all the known (given) quantities, this becomes$$0=(100\text{kg})(0.05\text{m/s})+(10\text{kg}){v}_{tk}$$Simplifying and rearranging yields v_{tk} = −0.5 m/s. Answer: Dmitry has to eject the toolkit at a speed of 0.5 m/s, or 50 cm/s. Note that this is 10 times Dmitry’s required speed. That’s precisely what one would expect, since Dmitry and his suit have 10 times the mass of his toolkit.


During the spacewalk described above, Dmitri tosses his detachable 10 kg toolkit. The statements below refer to Dmitri and the toolkit during the throw. Decide whether each statement is true or false.
 The magnitude of the force is the same for each.
 The duration of the event is the same for each.
 The magnitude of the acceleration is the same for each.
 The magnitude of the impulse is the same for each.

Answer: True, since these forces are an action–reaction pair.
 True, because the forces act on each object simultaneously.
 False, because the masses are not equal. Dmitri has a greater mass than the toolkit, and therefore his acceleration will be less.
 True. The impulses must be equal since the forces and durations are equal.

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