Implse and collisions

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In summary, the problem involves two ice skaters colliding into each other, with skater 1 (mass 58.96 kg) traveling at 7.15 m/s and skater 2 (mass 49.89 kg) at rest. Skater 1 pushes skater 2 with an average force of 1300 N over a period of .75 seconds. Using the equation for impulse, we can determine the final velocities of both skaters after the impact. However, it is important to note that the force imparted by skater 1 on skater 2 is an internal force and does not contribute to the momentum change of the center of mass of the two skaters.
  • #1
loatisaf
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impulse and collisions

I have one problem I've been trying to do, but I'm stuck on it. In this one, two ice skaters collide into each other. The specifics are as follows:
Skater 1 (mass 58.96 kg) is traveling at 7.15 m/s. She then collides with skater 2 (mass 49.89 kg) who is at rest. During the collision, skater 1 pushes skater 2 as hard as she can, imparting an average force of 1300 N over a period of .75 seconds. The questions are how fast are skater 1 and skater 2 moving after the impact.

I 've got the whole force over time thing is impulse, so I've got that
(m1v1f + m2v2f) - (m1v1i + m2v2i) = 975
and breaking it down, collecting like terms, and inserting values I already know, it works out to
5896 v1f-49.89 v2f = 1396.564
Unfortunately, this formula still has 2 unknown values, and I can't think of a second formula to use to do substitution.
 
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  • #2
Your formula is incorrect!
The force imparted by skater 1 one skater 2 is an INTERNAL FORCE, hence, it does NOT contribute to momentum change of the center of mass of the 2 skaters.
The correct set of equations are therefore:
[tex]m_{1}v_{1,f}+m_{2}v_{2,f}-(m_{1}v_{1,i}+m_{2}v_{2,i})=0[/tex]
[tex]m_{2}v_{2,f}=975[/tex]
 
  • #3
arildno's solution is, of course, completely correct. But a slightly simpler set of equations can be obtained by realizing that the skaters exert equal and opposite forces on each other:
[tex]m_{1}v_{1,f} -m_{1}v_{1,i} =-975[/tex]
[tex]m_{2}v_{2,f}=975[/tex]

But most important is to understand that both methods are valid and equivalent.
 
  • #4
I agree; using Newton's 3.law in an explicit manner is more straightforward
 

1. What is the difference between impulse and momentum?

Impulse is the change in momentum of an object over a period of time, while momentum is the product of an object's mass and velocity. Impulse is a vector quantity while momentum is a scalar quantity.

2. How does the impulse-momentum theorem relate to collisions?

The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. In collisions, the impulse experienced by each object involved is equal and opposite, resulting in a change in momentum for both objects.

3. Can the conservation of momentum be violated in collisions?

No, the conservation of momentum is a fundamental law of physics that states that the total momentum of a system remains constant in the absence of external forces. This means that in collisions, the total momentum of all objects involved before and after the collision must be equal.

4. How do elastic and inelastic collisions differ in terms of impulse and momentum?

In elastic collisions, both momentum and kinetic energy are conserved, meaning there is no loss of energy. In inelastic collisions, some kinetic energy is lost, resulting in a decrease in momentum. However, both types of collisions still follow the law of conservation of momentum.

5. How can impulse be calculated in a real-life scenario?

In a real-life scenario, impulse can be calculated by measuring the force applied to an object over a period of time. The impulse is equal to the force multiplied by the time interval over which the force is applied. This can be represented by the equation J = FΔt.

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