BR physics chapter 4

[2010premed]

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I'm a little confused about how these answer are reconciled...

#6 page 203: If the child need to get back to her starting point, which of the following would allow her to do this?:
Answer: throwing her oversized hat away from the sled
explanation: by conservation of momentum, if the child thrown her hat away from the sled and to the right, then she and the sled will move left, toward the starting point. If the momentum of the child/sled system is 0 before the child throws the hat, then after the hat is thrown, the total momentum must still be zero. If the hat moves in 1 direction, then the sled must move in the opposite direction.

#46 page 214: two cars collide inelastically at a North-South East-West intersection. The skid marks point roughly northwest. Concerning the inital directions of the 2 cars, this tells you that one driver was travelling:
A: west; the other driver was travelling north.
Explanation: Momentum is a vector quantity. Conservation of momentum must conserve magnitude aswell as direction. The final direction must therefore reflect the initial direction.

#48 page 214: A large trck, traveling due south with speed v, collides with a small car traveling due north with the same speed v. After the collision, the car is moving due east, with the same speed it had prior to the collision. What can you conclude about the final velocity of the track?
A: It points southwest

 

[loveoforganic]

Where are you confused? Do you feel the answers contradict each other? Sorry, I'm not sure what you mean by reconciled. I can explain these answers, but it'd be a bit of work (drawing and scanning), so I want to make sure I know where you're confused first.

 

[2010premed]

hey yes it see,ed like the answer explanation contradict each other and I cant get a pattern down

 

[loveoforganic]

I'll only draw if I have to ;P

Momentum is always conserved. Momentum is vectorial.

For the first one, you start with a momentum of zero. The person tosses the hat. The hat carries a certain amount of momentum, mass hat times velocity hat. To conserve momentum, the person must travel with a velocity in the direction opposite the hat at a speed that will equal out the momentums. So the person will be moving slower than the hat in the opposite direction.

For the second one, your skidmarks point NW, so that implies that's the direction your cars are moving after the collision. Therefore, your final momentum is pointing NW. Since momentum is conserved, the combined momentums of the cars prior to collision must also be pointed NW. So look for the combination that adds up correctly vectorially. One car moves north, the other moves west.

For the third one, the masses are important. The truck and car are moving the same speed, but the truck is bigger, so it has more momentum. Their directions prior to collision are opposite, truck goes south, car goes north. So the net momentum is pointing due south. After the collision, the car is going due east. To obtain a net momentum of due south (the initial momentum), the truck must cancel out the car's eastward momentum (it goes to the west some) and it must add some southward momentum (it goes to the south some) - so the truck's final motion is southwest.