# When to use Momentum vs When to use K.E.

• Konner54
In summary, momentum is always conserved, but energy may or may not be conserved in collisions between objects.
Konner54
Homework Statement
A 20kg Cart is moving horizontally along a friction-less track with a speed of 4 m/s when a 10 kg bag of sand is quickly placed on it. What is its new speed?
Relevant Equations
1/2mv^2 and P=mv
Hi Folks,

This is a super simple physics problem that I just cannot understand when and where to implement the difference. Here is the problem:

A 20kg Cart is moving horizontally along a friction-less track with a speed of 4 m/s when a 10 kg bag of sand is quickly placed on it. What is its new speed?

I attempted solving this by assuming that the kinetic energy before and after must be the same, thus:

1/2 Mi Vi^2 = 1/2 Mf Vf^2. Solving for the final velocity I got 3.26 m/s

However, the correct answer is ¨¨¨~2.7 m/s, derived by using the conservation of momentum:

MiVi=MfVf. Solving for the final velocity.

Shouldn't these values be the same in a completely elastic collision such as this? What am I missing?

Any insight on when to deploy KE and when to deploy conservation of P would be great.

Thanks!

Assuming that the bag of sand stays on the cart, the collision is not elastic. The bag of sand absorbs energy in the collision. If the collision were elastic, then the two colliding objects would go their separate ways and both energy and momentum would be conserved.

PeroK, Konner54 and phinds
tnich said:
Assuming that the bag of sand stays on the cart, the collision is not elastic. The bag of sand absorbs energy in the collision. If the collision were elastic, then the two colliding objects would go their separate ways and both energy and momentum would be conserved.

Konner54
On top of #2: Momentum is always conserved as long as there are no external forces acting on your system. Kinetic energy may or may not be conserved depending on whether or not the collision is elastic. If two objects stick together, the collision is not elastic.

The problem as written down is also incomplete as it presumes the sand bag has zero velocity before being placed, this is an assumption that should be stated.

Konner54
tnich said:
Assuming that the bag of sand stays on the cart, the collision is not elastic. The bag of sand absorbs energy in the collision. If the collision were elastic, then the two colliding objects would go their separate ways and both energy and momentum would be conserved.
Thankyou! I was unaware that two objects sticking together did not mean it was elastic - I just assumed that it could be considered as a single entity after the addition of the sand.

Orodruin said:
On top of #2: Momentum is always conserved as long as there are no external forces acting on your system. Kinetic energy may or may not be conserved depending on whether or not the collision is elastic. If two objects stick together, the collision is not elastic.

The problem as written down is also incomplete as it presumes the sand bag has zero velocity before being placed, this is an assumption that should be stated.
This is actually for a medical school entrance exam and sadly, the questions are often painfully incomplete (in an attempt to trip you up).
Thank you for the insight! I will remember this for next time.

Konner54 said:
Thankyou! I was unaware that two objects sticking together did not mean it was elastic - I just assumed that it could be considered as a single entity after the addition of the sand.

The important point is that momentum is always conserved. You can use that not only to solve the problem but also to show that energy must be lost in this case. You don't have to assume or guess that energy is not conserved. You can, in fact, calculate how much energy is lost, by using conservation of momentum.

PeroK said:
The important point is that momentum is always conserved.
But it is conserved unless an external force acting on it?In this case a sand bag is placed suddenly.Then there must be a force exerted by sandbag on the cart.

hyunxu said:
But it is conserved unless an external force acting on it?In this case a sand bag is placed suddenly.Then there must be a force exerted by sandbag on the cart.
Yes, it is conserved in a given direction within a system if there are no external forces on that system with a component in that direction.
In the present case, we are considering the system consisting of the sandbag and the cart.

hyunxu said:
But it is conserved unless an external force acting on it?In this case a sand bag is placed suddenly.Then there must be a force exerted by sandbag on the cart.
We are considering the full system including both sand bag and cart. The forces between the sand bag and the cart are internal to that system and so do not affect the total momentum.

hyunxu
hyunxu said:
But it is conserved unless an external force acting on it?In this case a sand bag is placed suddenly.Then there must be a force exerted by sandbag on the cart.
The momentum of the cart reduces by exactly the amount of momentum gained by the bag.

That's conservation of momentum.

If, instead, energy were conserved that would imply an increase in total momentum of cart plus bag (Do the calculations). And that increase in momentum would need to be explained.

Last edited:
hyunxu

## 1. When should I use momentum and when should I use kinetic energy?

Momentum and kinetic energy are both important concepts in physics that are often used interchangeably. However, they have distinct meanings and should be used in different situations. Momentum is a measure of an object's motion and is useful when studying collisions and interactions between objects. On the other hand, kinetic energy is a measure of an object's energy due to its motion and is useful when studying the work done by a force. Therefore, momentum should be used when analyzing interactions between objects, while kinetic energy should be used when analyzing the work done on an object.

## 2. What is the difference between momentum and kinetic energy?

As mentioned before, momentum is a measure of an object's motion, while kinetic energy is a measure of the energy due to its motion. Momentum is a vector quantity, meaning it has both magnitude and direction, while kinetic energy is a scalar quantity, meaning it only has magnitude. Additionally, momentum is conserved in a closed system, while kinetic energy is not necessarily conserved.

## 3. Can momentum and kinetic energy be used interchangeably?

No, momentum and kinetic energy cannot be used interchangeably. As mentioned before, they have distinct meanings and should be used in different situations. Using the wrong concept can lead to incorrect interpretations and results.

## 4. In which situations is momentum more useful than kinetic energy?

Momentum is more useful than kinetic energy in situations where interactions between objects are being studied. For example, in collisions, momentum is conserved, and analyzing the momentum of each object can help determine the outcome of the collision. In these situations, kinetic energy may not be conserved due to external forces acting on the objects.

## 5. When should I use kinetic energy instead of momentum?

Kinetic energy should be used instead of momentum when studying the work done by a force on an object. This is because kinetic energy is directly related to the work done on an object by a force. Additionally, kinetic energy can also be used to determine the speed of an object, which can be useful in certain situations where momentum may not provide enough information.

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