Thinking Physics Question 3

1) The speed of the car will
(b) decrease

2) The momentum of the car will
(a) increase

3) And the kinetic energy of the car will
(c) not change

The rain has now stopped. A drain plug is opened in the bottom of the rolling car allowing the accumulated water to run out. Consider the effects of the draining water on the speed, momentum, and kinetic energy of the rolling car.

4) The speed of the car will
(a) increase

5) The momentum of the car will
(b) decrease

6) And the kinetic energy will
(c) remain the same

Assuming the only affect the water has on the train is to change its mass, this is conservation of energy, and you can just use KE = 1/2(m)(v^2). So energy stays the same regardless, velocity is inversely related to mass, and because energy depends on v^2, momentum, L = mv won't be conserved .

1b)it needs to move accelerate the vertical water, which it does effectively by colliding with it.
2c) the overall momentum of the car + contained water will not change, because the water has no horizontal momentum, and it must be conserved.
3b)for the car+contained water, mv=momentum, unchanging, v decreases. E=mv*v/2 so E decreases.
4a) nothing acts on the car +contained water, so it must stay the same velocity.
5b) for the car + contained water: it loses water, so therefore the momentum stored in that water.
6b) energy in the escaping water is not counted in the car+water, so for the car+water, it decreases.

b) decrease.....if it stayed the same or sped up, it would have more energy than it initially had

c) not change...the momentum of the entire system is constant.

b) decrease.....inelastic collision

c) remain the same....the rain is in the train's frame of reference and just free falling

b)decrease..less mass same speed

decrease...less mass same speed

fuck, i know I got it wrong. Forgot the friction between the car and the rain, which exerts the horizontal force that slows the car down.

4c) nothing acts on the car +contained water, so it must stay the same velocity.

1. C The speed will not change because velocity is not affected by mass, though force and acceleration are. The only reason that things slow down when big stuff are put on them is because of the normal force and friction, but this is a frictionless railroad car.

2. A The momentum of the car will increase as the mass increases.

3. A The kinetic energy of the car will increase as the mass increases.

For both of 2 and 3, though, where does the new momentum and KE come from...

4. C Once again, the speed will not change because the velocity is not affected by the mass.

5. B Less mass = less momentum...

6. B Less mass = less kinetic energy... goddamnit I know this doesn't even make any sense...

Geez hmm... i may edit my answer.

I'll go with my gut and likely get tricked again

1) C - Not change. The car is rolling without friction so nothing is slowing it down, and the rain is falling vertically so I don't think it'll cause a deceleration
2) C - I'm not sure if the water counts, so I'm gonna say no it doesn't, and the momentum of the car itself should be the same
3) C - as above

4) C - Same as 1
5) C - Same as 2
6) C - Same as 3

I like my answers, nice and uniform

1. c
2. a
3. a

4. c
5. b
6. b

1. Decrease. Could see raindrops as moving backwards inside the car until they hit the back end, at which point they exert a backwards force on the car until they have accelerated to the car's velocity (while decelerating the car a tiny amount - energy ain't free).

2. Some of the momentum has transferred to the raindrops (the mass of the car itself is unchanged, but its speed is lower), so it decreased.

3. The car lost kinetic energy to the raindrops while accelerating them.

4. Remain the same - the car won't speed back up; the draining water is moving at the same rate as the car and won't "give back" the speed. This is neglecting the possibility that the drain is not centered on the center of mass of the water, which actually would change the car's velocity but in a way that is unknowable without knowing the location of the drain.

5. Well, the mass of the car isn't changing, nor is its speed. The momentum is the same.

6. Nothing is accelerating or decelerating the car. The kinetic energy is the same.

1. Decrease. The newly acquired raindrops are falling straight down, so they are accelerated by the car to the car's velocity. This decreases the speed.

2. Increase. P = mv, and m is increasing while v is decreasing. However, m increases at a linear rate and v decreases at an inverse proportion to m (e = 1/2 * mv^2).

3. Energy ain't going anywhere...

4. Assuming the drain plug is centered on the car's water holding volume's center of mass in the XY plane, the draining water won't accelerate the car in any direction. Or more precisely, the acceleration of the remaining water inside the car towards the drain will be a net 0. Thus, the force exerted by said water on the car is 0, and the car's velocity does not change.

5. Mass is decreasing while v is constant, so the momentum decreases.

6. Same argument; energy decreases.

Hmm wait, theres no way it could speed up after draining the water, i'm pretty sure about the rest of my answers though.

Some definitions should be made. First when i talk about car i mean car itself and water in the car, under the term kinetic energy of the car i understand energy related with the motion of the center of the mass. And it looks like sentense 'Consider the effect of accumulating rain on ...' implied that all droplet hitting the car will be retained (but it is not clear).

Lets begin with momentum. As far as all droplets will get into the car there will not be any internal forces so the momentum of droplets + momentum of car will not change. And considering that droplets had no horizontal component of momentum (when they were not part of the system) we can conclude that momentum of the car will not change.
The mass of the car will increase and the momentum will not change it means that velocity will decrease.
It is easuy to show that kinetic energy wil also decrease because part of it will transform into internal energy (if collisions with droplets are inelastic) or into the wave energy (if collisions are elastic).
In the second part we assume that all energy was dissipated and there are no waves inside the car otherwise the answer would be dependant on the way of draining.

The velocity will not change because if the plug in the bottom there will not be any additional forces. Momentum and kinetic energy will decrease because part of it will be taken out with water.
1)b
2)c
3)b
4)c
5)b
6)b