Finding Final Velocity of Mass 1 After Collision

In summary, the problem involves two masses, 2.77 kg and 1 kg, with initial velocities of (1i - 1j) and 0 respectively. After a collision, the second mass moves with a velocity of (2i - 3j). The final velocity of the first mass is unknown. The equations for conservation of momentum and kinetic energy can be used to solve for the final velocities, but the final velocity of the first mass may not necessarily be equal to the initial velocity.
  • #1
Nicki
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Homework Statement


Mass 1 (2.77 kg) moves with an initial velocity (1i - 1j) and mass 2 (1 kg) starts at rest. After the collision, M2 moves with a velocity of (2i - 3j). What is the final velocity of m1?

Homework Equations


Since they don't stick together, KE and linear momentum are conserved.
M1V1ix + M2V2ix = M1V1fx + M2V2fx

M1V1iy + M2V2iy = M1V1fy + M2V2fy

1/2 M1V1i^2 + 1/2M2V2i^2 = 1/2 M1V1f^2 + 1/2M2V2f^2

V1f = (sqrt)V1xf^2 + V1yf^2

The Attempt at a Solution


I don't really understand these problems, and we had a substitute professor into teach this, so here goes nothing, literally.
2.77 (1) + 0 = 2.77 Vx + 1(2) Vx = 0.278 m/s ?
2.77(-1) + 0 = 2.77 Vy + 1(-3) Vy = 0.0.83 m/s ?

This doesn't seem right? Shouldn't I need to use th equations for KE for an elastic collision?
 
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  • #2
Nicki said:
Since they don't stick together, KE and linear momentum are conserved.
No. Momentum is conserved, but loss of some KE does not necessarily mean the objects coalesce. That is only the extreme case, in which the KE lost is maximised.
 

1. What is the formula for finding the final velocity of Mass 1 after a collision?

The formula for finding the final velocity of Mass 1 after a collision is: v1f = (m1v1i + m2v2i) / (m1 + m2), where v1f is the final velocity of Mass 1, m1 is the mass of Mass 1, v1i is the initial velocity of Mass 1, m2 is the mass of Mass 2, and v2i is the initial velocity of Mass 2.

2. What is the difference between an elastic and inelastic collision?

In an elastic collision, both kinetic energy and momentum are conserved, meaning that the total energy and momentum of the system before and after the collision are the same. In an inelastic collision, only momentum is conserved, and some of the kinetic energy is lost, usually in the form of heat or sound.

3. How do you determine the mass and velocity of each object after a collision?

To determine the mass and velocity of each object after a collision, you need to know the initial mass and velocity of each object, as well as the type of collision (elastic or inelastic). Using the conservation of momentum and/or kinetic energy equations, you can solve for the final velocities of each object and then use the mass and velocity equations to determine the final mass of each object.

4. Can the final velocity of Mass 1 ever be greater than its initial velocity after a collision?

Yes, the final velocity of Mass 1 can be greater than its initial velocity after a collision in certain situations. This can happen in an elastic collision when Mass 1 has a smaller mass than Mass 2 and Mass 2 has a greater initial velocity. In this case, Mass 1 will gain some of the kinetic energy from Mass 2 and have a final velocity that is greater than its initial velocity.

5. Are there any real-life applications of calculating the final velocity of an object after a collision?

Yes, there are many real-life applications of calculating the final velocity of an object after a collision. This concept is used in car accidents to determine the speed of the vehicles involved, in sports to analyze the impact of collisions between players, and in engineering to design safety features for buildings and vehicles. It is also important in understanding the behavior of particles in particle colliders and the dynamics of celestial bodies in space.

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