Velocity and frame of reference question

In summary, the conversation is discussing a problem involving two cars colliding elastically. The total masses and velocities of the cars are given, and the task is to calculate their final velocities after the collision. The equations mentioned are 9.22 and 9.23 for analyzing the collision in a specific reference frame, and equations 9.16 and 9.15 to show conservation of kinetic energy and linear momentum in that same reference frame. The question also asks for the final velocities in the Earth's reference frame and to prove conservation of kinetic energy and linear momentum in that frame as well. The main concept being tested is energy conservation and its application in different reference frames.
  • #1
Pepsi24chevy
65
0
Hey I am just lookin for some guidance here of what equations to use for this problem. My teacher gave us likea hint, but the hints are from the book used in the previous course and since i am a transfer stuident, i do not have this book. Anyway the question goes as followed...

You are driving a bumper car (total mass = 155 kg) at +12.0 m/s in the positive x-direction (in the reference frame of the Earth), toward your friend (in his bumper car, total mass 125 kg) who is driving in the same direction at +6.00 m/s (in the reference frame of the Earth). You collide elastically.

To get you started, in your reference frame (a reference frame in which you are at rest with v = 0), the initial velocity of your friend (before the collision) is -6.00 m/s; you see your friend coming toward you (negative x-direction) at 6.00 m/s.

A) In your friend's reference frame (a reference frame in which your friend is at rest), what is your initial velocity (before the collision)?

B) Analyze the collision in your (initial) reference frame (moving at +12.0 m/s in the x-direction with respect to the reference frame of the Earth). What are the final velocities (after the collision) of you and your friend in this reference frame? You can use eqns. 9.22 and 9.23 in the text for this.

C) Show that the total kinetic energy of you and your friend was conserved in this reference frame, i.e. that equation 9.16 in the text is true.

D) Show that the total linear momentum of you and your friend was conserved in this reference frame, i.e. that equation 9.15 in the text is true.

E) In the reference frame of the Earth, what are the final velocities (after the collision) of you and your friend? You may simply transform the velocities you calculated in (B) back to the Earth's reference frame.

F) Show that the total kinetic energy of you and your friend was conserved in the Earth's reference frame.

G) Show that the total linear momentum of you and your friend was conserved in the Earth's reference frame.

I am just lookin for some guidance of which equations i need to be lookin at for parts B, C, F, and G. Thanks
 
Physics news on Phys.org
  • #2
By definition elastic collision implies that kinetic energy is conserved. Hence I couldn't understand the meaning in the question C and F. Can anyone explain? Is the need to verify the formula of finding final velocities after elastic collision.
 
  • #3
vaishakh said:
By definition elastic collision implies that kinetic energy is conserved. Hence I couldn't understand the meaning in the question C and F. Can anyone explain? Is the need to verify the formula of finding final velocities after elastic collision.

I think the question is hinting in that Energy conservation applies no matter what frame of reference you use. So its asking you to prove it.

Sam
 
  • #4
I think you know what is elastic collision. You can write two equations for elastic collisions.
M1u1 + m2u2 = m2v2 +m1v1 – momentum conservation
M1u1^2 + m2u2^2 = m1v1^2 + m2v2^2 – energy conservation
Try to solve these simultaneous equations and get v1 and v2 with respect to m1, m2, u1 and u2.
 

1. What is velocity?

Velocity is a measure of the rate of change of an object's position with respect to time. It is a vector quantity, meaning it has both magnitude and direction.

2. How is velocity different from speed?

Velocity and speed are often used interchangeably, but they have different definitions. While velocity includes direction, speed is a scalar quantity that only measures the magnitude of an object's motion.

3. What is frame of reference?

Frame of reference is a coordinate system used to describe the position and motion of an object. It is the perspective from which an observer measures and describes an object's motion.

4. How does the frame of reference affect velocity?

The frame of reference can affect the measured velocity of an object. If the observer is in a different frame of reference, they may perceive the object's velocity to be different due to their own motion or perspective.

5. Can an object have different velocities in different frames of reference?

Yes, an object can have different velocities in different frames of reference. This is because the frame of reference affects the perception of an object's motion, but the object's actual velocity remains constant.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
859
  • Introductory Physics Homework Help
Replies
6
Views
891
  • Introductory Physics Homework Help
Replies
2
Views
908
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
5K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Replies
12
Views
616
  • Introductory Physics Homework Help
Replies
6
Views
954
Back
Top