Momentum Conservation

[texan2414]

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388 + 389 in EK 1001 Physics---

Bucket full of water is slid across a sheet of ice (frictionless) in the rain

A) What happens to velocity and momentum as the bucket fills with rainwater as it slides?
B) What happens to velocity and momentum if bucket develops a leak as it slides?

My answer and reasoning:
A) Since momentum is a conserved in a system, I thought that as it fills its mass would increase but to conserve momentum, the velocity would decrease.
B) Since momentum is conserved in a system, I thought that as it leaks, its mass would decrease so its forward velocity has to increase to compensate for the loss of mass.

My reasoning rests on the fact that momentum is conserved in a system. However, the answer is:

A) velocity remains constant; momentum increases.
B) velocity remains constant; momentum decreases.

I don't understand why momentum is not conserved in this scenario- Any explanations would be helpful.

Thanks,

 

[monkeyvokes]

for A, i think it's because you're adding mass from outside the system. The additional mass falls vertically down into the bucket without contributing to horizontal velocity.

for B, maybe no velocity change because water just leaks out. There is no acceleration ?

I'm not sure if this is the best explanation, hopefully someone else will have a better resolution?

 

[monkeyvokes]

I like how these EK problems are sometimes tricky like this. They really get you thinking about the physics behind these situations, making you more familiar with concepts (and so you can answer the easier questions much faster).

 

[The_Sunny_Doc]

388 + 389 in EK 1001 Physics---

Bucket full of water is slid across a sheet of ice (frictionless) in the rain

A) What happens to velocity and momentum as the bucket fills with rainwater as it slides?
B) What happens to velocity and momentum if bucket develops a leak as it slides?

My answer and reasoning:
A) Since momentum is a conserved in a system, I thought that as it fills its mass would increase but to conserve momentum, the velocity would decrease.
B) Since momentum is conserved in a system, I thought that as it leaks, its mass would decrease so its forward velocity has to increase to compensate for the loss of mass.

My reasoning rests on the fact that momentum is conserved in a system. However, the answer is:

A) velocity remains constant; momentum increases.
B) velocity remains constant; momentum decreases.

I don't understand why momentum is not conserved in this scenario- Any explanations would be helpful.

Thanks,

You're right. 🙂 Momentum is conserved, and velocity decreases as the rain bucket fills, assuming the rainwater is falling straight down into the bucket.

In the second scenario, however, momentum is not conserved since the rainwater is taking some of that horizontal momentum with it. In that case, momentum would decrease. Velocity would be constant since v= p/m. Momentum decreases by the same amount as the mass of the water-filled bucket decreases, so velocity is unchanged.

 

[texan2414]

Actually sunnyd, for part A, momentum increases where velocity remains constant.