Elastic Collision in Two Reference Frames

  • #1
18
1

Homework Statement


1. Two skateboarders start from rest on opposite sides of a ramp like the one in the image, roll down and collide elastically on the level part of the ramp. The masses of the skateboarders are m1 = 48 kg and m2 = 55 kg and they both start from the height h = 4.70m. Ignoring any friction, calculate the maximum heights that each skateboarder reaches after the collision
(a) by performing the collision calculation in the laboratory frame
(b) by performing the collision calculation in the centre of momentum frame
skate%20ramp3_001.jpg

Homework Equations


Conservation of energy/momentum
1/2mv2 = mgh
mvi = mvf

The Attempt at a Solution


I worked out the velocity and momentum of each skater at the instant before they collide, thinking that I could then use normal conservation of momentum and energy to work out the same values for afterward, but as I reached this point I realised that I do not know how to proceed because I have no final values to substitute into the post-collision equation, so do not know how to proceed from here. In the lab frame I have calculated the pre-collision momentum of skater 1 to be 460.8kgm/s, and skater 2 to be 528kgm/s
 

Attachments

  • skate%20ramp3_001.jpg
    skate%20ramp3_001.jpg
    10.2 KB · Views: 259

Answers and Replies

  • #2
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
17,343
7,214
Please show what you have done.
 
  • #3
713
275
Velocity of both skateboarders on collison will be √(2gh). Both experience the same change in momentum Δp = 2μΔv (elastic collision) where μ is their reduced mass [m1*m2/(m1+m2)] and Δv is their relative velocity = 2√(2gh). Simply subtract Δp from the respective momentums and then divide by respective masses to obtain respective velocities. Finally use h = v^2/(2g).
 

Related Threads on Elastic Collision in Two Reference Frames

Replies
6
Views
8K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
4
Views
9K
  • Last Post
Replies
5
Views
10K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
5K
P
  • Last Post
Replies
13
Views
2K
Replies
2
Views
769
  • Last Post
Replies
2
Views
778
Top