Momentum, Impulse, and Collision

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Homework Help Overview

The problem involves two skaters on a frictionless circular rink who push off each other and move apart. Given the time taken for each skater to reach the edge of the rink, the goal is to determine the mass of the second skater based on the principles of momentum and impulse.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the skaters' speeds and the distances traveled, questioning how to incorporate the unknown distance into their calculations.
  • Some participants express confusion over the validity of the equations being used, while others suggest that the distances can cancel out in the momentum equation.
  • There is a consideration of whether initial velocities and forces should be factored into the problem, with some participants exploring the implications of impulse.

Discussion Status

The discussion is ongoing, with various interpretations of the problem being explored. Some participants have provided guidance on how to set up the equations, while others are questioning the assumptions made about forces and initial conditions. There is no explicit consensus on the approach to take, but productive dialogue is occurring.

Contextual Notes

Participants note that the problem does not provide specific distances or initial velocities, leading to discussions about how these factors might influence the calculations. The context of the skaters being in a frictionless environment is also acknowledged.

Tastosis
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Homework Statement


Two skaters stand in the center of a circular rink of frictionless ice. When the skaters push on one another, they move apart along the same straight line. If the skater of mass m1 = 50 kg reaches the edge of the rink after 12 seconds and the other skater reaches the opposite edge of the rink in 18 seconds, what is the mass m2 of the second skater?


Homework Equations


M1V1 + M2V1 = M1V2 + M2V2 ?


The Attempt at a Solution


How do I get the mass if the distance is not given?
 
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They traveled the same distance.Find the ratio of the speeds.

ehild
 
I'm confused >.<

So the equation I'm using is wrong?
 
no there is no problem with the equation.
let the distance moved be x and then solve. It will get cancelled.
 
50kg * x/12s+ M2 * x/18s = 50kg * x/12s + M2 * x/18s ?
 
Tastosis said:
I'm confused >.<

So the equation I'm using is wrong?

It is not wrong, only it does not mean anything. Both sides are identical, so you say that something is equal with itself. What did you want to state with that equation?

ehild
 
50kg (1/12s) + M2 (1/18s) = 0

M2 = [50kg (1/12s)] / 1/18s

M2 = 75kg

Did I do it right?
 
Tastosis said:
50kg (1/12s) + M2 (1/18s) = 0

M2 = [50kg (1/12s)] / 1/18s

M2 = 75kg

Did I do it right?

You made two mistakes and they canceled each other resulting in a correct mass. Your equation would result in a negative mass.

The skaters moved in opposite directions, one velocity is positive, the other is negative. So the correct equation is

m1 x/12 - m2 x/18 =0

Solving the equation correctly,

m1/12 = m2/18 , m2=m1 18/12 = 75 kg.

ehild
 
do we also have to consider the initial velocity and the amount of force pushed in a given time interval of 6 seconds?
 
  • #10
I do not get you. There is no question concerning the force between the skaters, setting them to move. It is assumed in such problems that the force acts for a very short time so the skaters are still very near to their original position when they are separated and move with some velocity. The difference between the times reaching the plank (6 s) comes from the different speeds the skaters move. ehild
 
  • #11
I was referring to the fact that Force times Time differenc is equal to the change in momentum. So, maybe you need to find initial velocity through that.
 
  • #12
Rayquesto said:
I was referring to the fact that Force times Time differenc is equal to the change in momentum. So, maybe you need to find initial velocity through that.

Read the problem: "Two skaters stand in the center of a circular rink" What is the initial velocity?

ehild
 
  • #13
Orginially I got 75 kg doing exactly what everyone else is doing, but I tried considering their small force. I know the answer is 75kg but I'm still skeptical about how like a reverse impulse can be tied into. that\s how my mind works though. I try to consider everything, but I still think the answer is 75 kg regaurdless of my skeptics.
 

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