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

[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!

 

[tnich]

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.

 

[phinds]

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.

 

[Orodruin]

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]

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.

 

[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.

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.

 

[PeroK]

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.

 

[hyunxu]

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.

 

[haruspex]

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.

 

[Orodruin]

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.

 

[PeroK]

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.