Calculating Speed in Elastic collision

In summary, in an elastic collision between a 15kg object moving at 3 m/s and a 10kg object at rest, the final velocities of the objects can be determined using the conservation of linear momentum and the conservation of kinetic energy equations. There will be a quadratic equation to solve, but the final velocities can be easily verified by checking the conservation of linear momentum and kinetic energy.
  • #1
connie5828
11
0

Homework Statement


An object of mass 15kg going to the right with a speed of 3 m/s collisdes with a 10kg object at rest. if the collision is ocmpletely elastic, calculate the speed of the 10kg object after collision


Homework Equations


m1vli +m2v2i=m1vlf+m2v2f


The Attempt at a Solution


I have tried plugging all the answers in and can't get the answer that is in the book. Also wondering if there is an easier way to get the answer. Also wondering if the # for at rest is 0
 
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  • #2
You have one equation and two unknowns. A second equation is needed to solve the problem. There are two relevant equations in elastic collision problems. One is the conservation of linear momentum, which you have stated. What is the other?
 
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  • #3
vli-V2i=-(Vlf-V2f)

is that correct?
Do you have to get the first one to get the speed of the 2nd one?
do you have to do the first equation I posted in order to do the 2nd equation?
 
  • #4
Conservation of kinetic energy. Do you know the equation for kinetic energy?
 
  • #5
KE=mv2/2

the info my professor gave showed no use of that formula though. I am now officially confused :)thanks for the help.
 
  • #6
Hmmm.

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter.

http://en.wikipedia.org/wiki/Elastic_collision
 
  • #7
ok, reading that was helpful. To get the 2nd speed would this be the equation?
0(10-15) + 2*15*3/10+15
I put 0 as the 10K object is at rest. Is that correct?
 
  • #8
I didn't solve the problem completely, but what you have doesn't offhand look right. You have two equations, the 2nd one containing velocity squared terms:

1. total linear momentum = const

2. total kinetic energy = const

In the end there will be a quadratic equation to solve (only one of the solutions being valid). The beauty of this problem is that it's easy to verify your answer. Once you determine the values of the final velocities of the objects, it's easy to verify that the total linear momentum and kinetic energy is indeed constant.
 

Related to Calculating Speed in Elastic collision

What is the formula for calculating speed in elastic collisions?

The formula for calculating speed in elastic collisions is v1f = (m1-m2)/(m1+m2) * v1i + (2*m2)/(m1+m2) * v2i, where v1f is the final velocity of the first object, m1 and m2 are the masses of the first and second objects respectively, v1i is the initial velocity of the first object, and v2i is the initial velocity of the second object.

What is an elastic collision?

An elastic collision is a type of collision between two objects in which both kinetic energy and momentum are conserved. This means that, after the collision, the sum of the kinetic energies of the two objects is the same as it was before the collision, and the sum of the momentums of the two objects is also the same.

What is the difference between elastic and inelastic collisions?

In an elastic collision, both kinetic energy and momentum are conserved, while in an inelastic collision, only momentum is conserved. In an inelastic collision, some of the kinetic energy of the objects is converted into other forms of energy, such as heat or sound.

How do you determine the initial and final velocities in an elastic collision?

The initial velocities can be measured before the collision occurs, and the final velocities can be calculated using the formula v1f = (m1-m2)/(m1+m2) * v1i + (2*m2)/(m1+m2) * v2i. The masses of the objects and their initial velocities are needed to calculate the final velocities.

Can the speed of an object change in an elastic collision?

Yes, the speed of an object can change in an elastic collision. This is because the final velocity is dependent on the initial velocities and masses of the objects involved in the collision. The speed of an object can increase, decrease, or remain the same after an elastic collision.

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