Question

the product of mass and velocity is momentum, p. the left side of the simplified equation you derived is the sum of the momenta of all objects in a system initially, $sigma p_i$. similarly, the right side of the simplified equation is $sigma p_f$. the fact that these two sums are equal to each other before and after objects interact is known as the law of conservation of momentum. the law states that the total momentum in a system is a conserved quantity. this means that while individual objects may undergo changes in their velocities and, therefore, changes in their momenta, the total amount of momentum in the system does not change. choose the correct answer from each drop-down menu to complete the statements. by the law of conservation of momentum, if object 1 gains momentum during a collision, then object 2 must dropdown momentum. each object’s mass is constant; therefore, whenever object 1 dropdown, object 2 slows down. the objects experience opposite accelerations, which is dropdown with newton’s third law.

Explanation:

1. For the first blank: According to the law of conservation of momentum, the total momentum of a system remains constant. So if object 1 gains momentum, object 2 must lose momentum to keep the total momentum the same.
2. For the second blank: Since mass is constant, momentum change is due to velocity change. If object 2 slows down (loses velocity, hence loses momentum), object 1 must speed up (gains velocity, hence gains momentum) to conserve total momentum.
3. For the third blank: Newton's third law states that for every action, there is an equal and opposite reaction. The opposite accelerations (due to forces from each other) are consistent with Newton's third law, so it is consistent.

Answer:

• By the law of conservation of momentum, if object 1 gains momentum during a collision, then object 2 must lose momentum.
• Each object’s mass is constant; therefore, whenever object 1 speeds up, object 2 slows down.
• The objects experience opposite accelerations, which is consistent with Newton’s third law.