# Conservation of Momentum Problem

• Avefan
In summary: So, in summary, the correct answer is (c) because both objects have the same momentum after the push due to the same applied force over the same period of time. Option (b) is not a plausible answer because the initial momentum of both objects is 0 and delta_p is the same as current_p since the initial_p is 0.

## Homework Statement

The same horizontal force is applied separately to two objects initially at rest on a horizontal, frictionless surface. Object A has less mass than object B. In each case the force is applied for the same length of time. Which of the following statements is true after the push?

(a) Object A has greater momentum than object B.
(b) Object B has greater momentum than object A.
(c) Object A has the same momentum as object B.
(d) Object A has the same kinetic energy as object B.
(e) Both objects have no momentum.

## Homework Equations

p = mv
delta_p = integral(F dt)

## The Attempt at a Solution

The answer key solution to this problems is option c with the explanation that "since the both objects are given the same force over the same period of time, F = dp/dt , delta_pa = delta_pb."
However, why is delta_p(change in momentum) the same as momentum and why isn't option (b) a plausible answer?

Avefan said:

## Homework Statement

The same horizontal force is applied separately to two objects initially at rest on a horizontal, frictionless surface. Object A has less mass than object B. In each case the force is applied for the same length of time. Which of the following statements is true after the push?

(a) Object A has greater momentum than object B.
(b) Object B has greater momentum than object A.
(c) Object A has the same momentum as object B.
(d) Object A has the same kinetic energy as object B.
(e) Both objects have no momentum.

## Homework Equations

p = mv
delta_p = integral(F dt)

## The Attempt at a Solution

The answer key solution to this problems is option c with the explanation that "since the both objects are given the same force over the same period of time, F = dp/dt , delta_pa = delta_pb."
However, why is delta_p(change in momentum) the same as momentum and why isn't option (b) a plausible answer?
Both objects start at rest so the initial momentum of both is 0 (i.e. initial_p=0). So at any time, delta_p = current_p - initial_p = current_p - 0 = current_p
Of course, (c) contradicts (b), so (b) can not be true.

## 1. What is conservation of momentum?

Conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant, regardless of any internal forces or interactions.

## 2. How is conservation of momentum applied in problem-solving?

In problem-solving, conservation of momentum is used to analyze the motion of objects involved in a collision or explosion. By applying the principle, we can determine the final velocities of the objects and understand the outcome of the interaction.

## 3. What are the conditions necessary for conservation of momentum to hold?

Conservation of momentum holds when there is no external force acting on the system and when the system is closed, meaning no mass is entering or leaving the system.

## 4. Can conservation of momentum be violated?

In classical mechanics, conservation of momentum is an absolute law and cannot be violated. However, in the quantum realm, there are instances where momentum can appear to be lost or gained due to uncertainties in measurements.

## 5. How does conservation of momentum relate to other conservation laws?

Conservation of momentum is closely related to other conservation laws, such as conservation of energy and conservation of angular momentum. These laws all stem from the fundamental principle of conservation of physical quantities in a closed system.