Elastic collisions in one dimension, unequal masses target at rest

In summary, the formula for elastic collisions in one dimension with unequal masses and a target at rest is derived using the conservation of momentum equation: m1u1 + m2u2 = m1v1 + m2v2. The student is having trouble getting the same formula as the one given in the book and needs help identifying where their algebra is incorrect. Deriving these formulas properly is important for solving future problems with different variables. The student has provided their attempted solution and the correct formula for reference.
  • #1
vinnyzwrx
15
0

Homework Statement



Derive formula for elastic collisions in one dimension, unequal masses target at rest.

i am having trouble acquiring the same formula that the book gives me, please tell me where my algebra is incorrect...

i need to be able to derive these formulas properly because in future problems i need to solve for different variables depending on the given data.

heres my work...

[URL]https://tdsal.homeserver.com/photos/photos%20hosted%20on%20internet/img_1457.jpg[/URL]

this is the correct formula, that i can't seem to get too.

[URL]https://tdsal.homeserver.com/photos/photos%20hosted%20on%20internet/img_1459.jpg[/URL]
 
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  • #2
Homework Equations conservation of momentum: m1u1 + m2u2 = m1v1 + m2v2The Attempt at a Solutionsee above
 

1. What is an elastic collision in one dimension?

An elastic collision in one dimension is a type of collision between two objects where both the momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy before and after the collision remain the same.

2. How do you determine if a collision is elastic in one dimension?

A collision is considered elastic in one dimension when the two objects involved do not stick together or deform during the collision. This can be determined by analyzing the final velocities of the objects after the collision. If the velocities are the same as the initial velocities, the collision is considered elastic.

3. What are unequal masses target at rest?

Unequal masses target at rest refers to a scenario in an elastic collision where one of the objects involved is significantly larger or heavier than the other and is initially at rest. This type of collision is commonly seen in sports such as billiards, where a heavier cue ball collides with a lighter target ball at rest.

4. How do unequal masses target at rest affect the outcome of an elastic collision?

In an elastic collision with unequal masses target at rest, the larger or heavier object will experience a smaller change in velocity compared to the lighter object. This is because the momentum of the larger object is greater, and therefore, it will transfer more momentum to the lighter object during the collision. However, the total momentum and kinetic energy of the system will remain the same.

5. What factors can affect the outcome of an elastic collision in one dimension with unequal masses target at rest?

The outcome of an elastic collision in one dimension with unequal masses target at rest can be affected by factors such as the initial velocities and masses of the objects, as well as the angle and point of impact during the collision. Other external factors such as air resistance or friction may also play a role in the outcome of the collision.

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