Kinetic energy and momentum (Conceptual Question)

[ScienceGeek24]

Homework Statement

The two toy cars shown in the figure, with masses as given in the figure, are ready to race. Both cars begin from rest. For each question, state whether the correct answer is car A, car B, or whether the two cars have equal values for the parameter in question.

For the next three parts assume that the cars’ motors supply the same force to each car over the course of a 1.0-meter race.

Car A mass= 1000g

Car B mass= 800g

I know that A) Which car crosses the finish line 1.0 away first?

=> Car B wins because it has less mass and more acceleration therefore more force.

B) Which car has the larger kinetic energy when it crosses the finish line 1.0 away?

=> Both cars have the same kinetic energy I know that both cars have the same kinetic energy because is a scalar , it does not depend in any other variable than energy. So they both have the same amount of kinetic energy.

C) Which car has a larger momentum when it crosses the finish line 1.0 away?

=> Car A because car A has a greater mass than car B they both have the same speeds therefore car A it will have more momentum.

D) Which car has traveled farther after 10^8 ?

=> Car B (I really don't get this one) (or why)

E) After 10^8 which car has a larger kinetic energy?

=> Car B (I really didn't understand this one nether)

F) After 10 which car has a larger momentum?

=> Both cars have the same momentum. (I don't know why both have the same momentum when they both have different masses and same velocity.)

Help? Can someone explain this to me?? please??

 

[PeterO]

Homework Statement

The two toy cars shown in the figure, with masses as given in the figure, are ready to race. Both cars begin from rest. For each question, state whether the correct answer is car A, car B, or whether the two cars have equal values for the parameter in question.

For the next three parts assume that the cars’ motors supply the same force to each car over the course of a 1.0-meter race.

Car A mass= 1000g

Car B mass= 800g

I know that A) Which car crosses the finish line 1.0 away first?

=> Car B wins because it has less mass and more acceleration therefore more force.

Your answer was going so well, and then you added "therefore more force" and spoiled it.B) Which car has the larger kinetic energy when it crosses the finish line 1.0 away?

=> Both cars have the same kinetic energy I know that both cars have the same kinetic energy because is a scalar , it does not depend in any other variable than energy. So they both have the same amount of kinetic energy.

Again, great opening 7 words but the reasoning is way off. Kinetic energy is gained when you do work on the cars. Work is force by distance. They were each subject to the same force. That force acted over a distance of 1 m.

C) Which car has a larger momentum when it crosses the finish line 1.0 away?

=> Car A because car A has a greater mass than car B they both have the same speeds therefore car A it will have more momentum.

Started out wrong this time, since you some how arrived at the idea that they have the same speed - which is wrong.

D) Which car has traveled farther after 10^8 ?

=> Car B (I really don't get this one) (or why)

travelled father after 10⁸ what?

E) After 10^8 which car has a larger kinetic energy?

=> Car B (I really didn't understand this one nether)

If that is really 10^-8 seconds these questions can start to make sense!

F) After 10 which car has a larger momentum?

=> Both cars have the same momentum. (I don't know why both have the same momentum when they both have different masses and same velocity.)

Again, if it is really 10^-8 this has meaning


Help? Can someone explain this to me?? please??

Comments above , and generally.

Work = Force x distance

Impulse = Force x time

Work leads to a change in KE on a flat surface
Impulse leads to a change in momentum.

Both these cars are subject to the same force, so variations in Work - KE and Impluse - momentum come about due to differeing distances and/or differing times.

The different masses mean B accelerates at a higher rate - will thus gain a higher speed, and cover a greater distance - in a given time.

If the "race" lasts only 1 metre, Car B, which has accelerated more quickly will win, because it is traveling faster.

Force x distance is the same for both cars; so Ke is the same

Force x time is greater for Car A, since it takes a greater amount of time to get there.

If the acceleration is carried out for a set amount of time, then the impulse applied to each is the same; so they have the same momentum.

In that time, B will have covered a greater distance, so the work done on B is greater than the work done on A; so B will have the greater KE. [remember; work = force x distance]

 

[ScienceGeek24]

Thanks! I can see now the meaning. Is just that i did not quite understood the concept of Work and impulse. Work is the change in KE on a flat surface and impulse is the change in momentum. It all seems clear now. Thanks man!

 

[PeterO]

Thanks! I can see now the meaning. Is just that i did not quite understood the concept of Work and impulse. Work is the change in KE on a flat surface and impulse is the change in momentum. It all seems clear now. Thanks man!

I mentioned the flat surface as sometimes these things happen on slopes, and part of the work goes to a change in Potential energy as well.

 

[asteriatic]

First of all, it's important to understand the concepts of kinetic energy and momentum. Kinetic energy is the energy an object possesses due to its motion, while momentum is the product of an object's mass and its velocity. Both are important concepts in the study of motion and are related to each other.

Now, let's address the questions one by one:

A) The correct answer is car B. This is because car B has less mass and therefore, less inertia, allowing it to accelerate faster and cross the finish line first.

B) The correct answer is both cars have the same kinetic energy. This is because kinetic energy is dependent on an object's mass and velocity, and both cars have the same velocity at the finish line.

C) The correct answer is car A. This is because momentum is directly proportional to an object's mass. Even though both cars have the same velocity, car A has a larger mass, giving it a larger momentum.

D) This question is a bit confusing and may not have a clear answer. It seems to be asking which car has traveled farther after 10 seconds, but it's not specified what happened during those 10 seconds. Assuming both cars were accelerating at the same rate, the answer would be both cars have traveled the same distance.

E) After 10 seconds, the answer would again be both cars have the same kinetic energy. This is because kinetic energy is not affected by the time taken to travel a certain distance, as long as the velocity remains constant.

F) After 10 seconds, both cars would have the same momentum. This is because momentum depends on both mass and velocity, and both cars have the same velocity at the 10 second mark.

I hope this helps clarify the concepts and answers your questions. Remember, it's important to understand the concepts behind these questions rather than just memorizing the answers.