Okay we have this problem: 50 kg mass traveling at 10 m/s strikes a 100kg mass at rest find the final velocity each....if...
1. it is elastic
2. if it isnt elastic
i know for an elastic something has to be 100% like 100% of momentum is conserved. I don't know how to set up equations for this logically i know 1/2mv^2 is Ke and mv=p
duplicate post. See my answer to the other post of the same question.
http://www.jiskha.com/display.cgi?id=1273626148
To solve this problem, we can apply the principle of conservation of momentum. The momentum before the collision should be equal to the momentum after the collision in both cases: elastic and inelastic.
Let's start with the elastic collision:
1. Elastic Collision:
In an elastic collision, both momentum and kinetic energy are conserved. To find the final velocities, we can set up equations using the conservation of momentum and the conservation of kinetic energy.
Conservation of momentum:
Before the collision:
Momentum of the 50 kg mass (m1) = m1 * v1
Momentum of the 100 kg mass (m2) = m2 * v2 (since it is at rest, the initial velocity v2 is 0)
After the collision:
Momentum of the 50 kg mass = m1 * v'1
Momentum of the 100 kg mass = m2 * v'2
According to the conservation of momentum, we have:
m1 * v1 = m1 * v'1 + m2 * v'2 (1)
Conservation of kinetic energy:
Kinetic energy of the 50 kg mass before the collision = 0.5 * m1 * v1^2
Kinetic energy of the 100 kg mass before the collision = 0.5 * m2 * 0^2
After the collision:
Kinetic energy of the 50 kg mass = 0.5 * m1 * v'1^2
Kinetic energy of the 100 kg mass = 0.5 * m2 * v'2^2
According to the conservation of kinetic energy, we have:
0.5 * m1 * v1^2 = 0.5 * m1 * v'1^2 + 0.5 * m2 * v'2^2 (2)
You can solve these two equations simultaneously to find the final velocities v'1 (velocity of the 50 kg mass after collision) and v'2 (velocity of the 100 kg mass after collision) in the elastic collision case.
2. Inelastic Collision:
In an inelastic collision, only momentum is conserved, not kinetic energy. The masses will stick together after the collision.
The conservation of momentum equation still remains the same as in the elastic collision:
m1 * v1 = (m1 + m2) * v' (3)
In this case, since the masses stick together, we only have one final velocity, denoted as v' (velocity of the combined mass).
You can solve equation (3) to find the final velocity v' in the inelastic collision case.
Remember to substitute the values of masses (m1 and m2) and initial velocities (v1 and v2) provided in the problem to get the final velocities.