Physics Help with elastic collision

In summary, Homework Equations a=rw Vr^2 states that the energy lost by a mass when it slides down a frictionless ramp is equal to the energy gained by the stationary mass.
  • #1
teresalin2004
2
0

Homework Statement


A mass 1.3 kg is initially at rest at the top of a 1.8 meter high ramp. It slides down the frictionless ramp and collides elastically with an unknown mass which is initially at rest. After colliding with the unknown mass, the 1.3 kg mass recoils and achieves a maximum height (altitude) of only 0.4 m going back up the frictionless ramp.
A.
Considering the energy of the 1.3 kg mass just before and just after the elastic collision, how much energy is lost by the 1.3 kg mass?
B.
What is the speed of the 1.3 kg mass just before the elastic collision?
C
What is the speed of the 1.3 kg mass just after the elastic collision?
D
Considering conservation of momentum, what is the momentum of the unknown mass just after the elastic collision?
E
What is the velocity of THE UNKNOWN mass before the elastic collision?
F What is the velocity of the unknown mass just after the elastic collision?
G
What is the mass of the unknown mass in kg?

Homework Equations


a=rw Vr^2
vf=m1v1+m2v2/ m1+m2

The Attempt at a Solution


vf=1.3*.04+1.3+1.8/ 1.2+1.8
1.8*1.3 - 1.2*0.4= 1.82 for Part A
So I know that the steps for B and C will be similar as will E and f but I have no idea how to get started
 
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  • #2
teresalin2004 said:

Homework Equations


a=rw Vr^2
What do you use that formula for? Do you know the formula for Kinetic Energy. They tell you that it slides down a frictionless ramp. This tells you that you don't lose any energy to friction. At the top of the ramp, what is the total energy (potential + kinetic)? How much is Potential Energy? How much is Kinetic?
At bottom of the ramp, what is the total energy? Potential is _____? Kinetic is _____?

Elastic collision means that total Kinetic energy before the collision is equal to total Kinetic energy after.
 
  • #3
One useful fact to keep in mind is that in an (linear) elastic collision of two objects is that
the relative speed of approach equals the relative speed of separation after the collision.
 
  • #4
Another method albeit going in the same direction as previous posts:

Energy lost by the falling mass (m1) = energy gained by stationary mass (m2).
Change in momentum (m1) = -(Change in momentum (m2))
2 equations , 2 unknowns: Solve to determine m (m2) and post collision v (m2).
 
  • #5
neilparker62 said:
Another method albeit going in the same direction as previous posts:

Energy lost by the falling mass (m1) = energy gained by stationary mass (m2).
Change in momentum (m1) = -(Change in momentum (m2))
2 equations , 2 unknowns: Solve to determine m (m2) and post collision v (m2).
I would say that is exactly the same as scottdave's approach, omitting his preliminary discussion about energy conservation.
J Hann's method is neater. It is a special case of Newton's Experimental Law. It is handy because it avoids the quadratic introduced by the KE equation.
 
  • #6
Hope I'm not missing something but other than determining pre collision and post collision velocity for m1 (√(2gh)) , no quadratic should be needed. The simultaneous equations can be solved by dividing Eqn 1 (KE) by Eqn 2 (momentum) eliminating m2 and leaving us with 1/2 v. Probably that's how we arrive at J. Hann's result in the first place.
 
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FAQ: Physics Help with elastic collision

What is an elastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. This means that the objects involved in the collision do not lose any energy and their velocities change only due to the exchange of momentum.

How is momentum conserved in an elastic collision?

In an elastic collision, momentum is conserved due to the fundamental law of physics called the law of conservation of momentum. This law states that the total momentum of a closed system (where no external forces are acting) remains constant before and after the collision.

What is the equation for calculating the velocities after an elastic collision?

The equation for calculating the velocities of two objects after an elastic collision is:v1 = (m1 - m2)u1 / (m1 + m2)v2 = 2m1u1 / (m1 + m2)Where m1 and m2 are the masses of the two objects, and u1 is the initial velocity of the first object.

Can an elastic collision occur between objects of different masses?

Yes, an elastic collision can occur between objects of different masses. In fact, this is the most common scenario for elastic collisions. The velocities of the objects after the collision will depend on their masses and initial velocities.

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

The main difference between an elastic collision and an inelastic collision is that in an inelastic collision, kinetic energy is not conserved. This means that the objects involved in the collision lose some energy, either in the form of heat or deformation. In an elastic collision, the objects do not lose any energy.

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