An object of mass 80kg moving with velocity 2m/s hit by collideswith another object of mass 20kg moving with velocity 4m/s find loss if energy assuming a perfectly inelastic collision
Were they going in the same or different directions?
In either case, momentum before = momentum after.
If collision is inelastic the stick together so use 100 kg for the mass on the right hand side.
For an elastic collision collision the total kinetic energy is conserved, when the collision is inelastic some of the kinetic energy is lost from the system while in a perfectly inelastic collision the two objects will stick together after the collision and move off together.
So, you need each objects initial mass and velocity, and the final velocity of the coMingling mass. Something is missing in your description.
energy lost= sum initial KEnergies-final KE energy
Given:
M1 = 80kg, V1 = 2m/s.
M2 = 20kg, V2 = -4m/s.
V3 = Velocity of M1and M2 after collision.
Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V3,
80*2 - 20*4 = 80*V3 + 20*V3,
100V3 = 80.
V3 = 0.80 m/s.
KEb = 0.5M1*V1^2 + 0.5M2*V2^2 = 40*4 +10*16 = 320 J. = KE before collision.
KEa = 40*0.8^2 + 10*0.8^2 = 32 J. = KE after collision.
KEb - KEa = 320 - 32 = 288 J. = KE lost.
To find the loss in energy in a perfectly inelastic collision, we can use the principle of conservation of momentum. In a perfectly inelastic collision, the two objects stick together and move as one after the collision.
First, we calculate the initial momentum of the objects before the collision using the equation: momentum = mass × velocity.
For the first object (80 kg, 2 m/s):
Momentum1 = 80 kg × 2 m/s = 160 kg·m/s
For the second object (20 kg, 4 m/s):
Momentum2 = 20 kg × 4 m/s = 80 kg·m/s
The total initial momentum before the collision is the sum of the individual momenta:
Total initial momentum = Momentum1 + Momentum2 = 160 kg·m/s + 80 kg·m/s = 240 kg·m/s.
Since the two objects stick together after the collision, their masses combine to form a single object with a mass of 80 kg + 20 kg = 100 kg.
Now, we calculate the final velocity of the combined object using the equation: momentum = mass × velocity.
Total final momentum = Total initial momentum = 240 kg·m/s.
Therefore, the final velocity of the combined object after the collision is:
240 kg·m/s = 100 kg × final velocity.
final velocity = 240 kg·m/s / 100 kg = 2.4 m/s.
Now, we can calculate the loss of kinetic energy. The initial kinetic energy (KE) before the collision is given by the equation: KE = 0.5 × mass × velocity^2.
Initial KE1 = 0.5 × 80 kg × (2 m/s)^2 = 160 J.
Initial KE2 = 0.5 × 20 kg × (4 m/s)^2 = 160 J.
The total initial kinetic energy is the sum of individual kinetic energies:
Total initial KE = Initial KE1 + Initial KE2 = 160 J + 160 J = 320 J.
The final kinetic energy of the combined object is given by:
Final KE = 0.5 × 100 kg × (2.4 m/s)^2 = 288 J.
Finally, we calculate the loss in energy:
Loss of energy = Total initial KE - Final KE = 320 J - 288 J = 32 J.
Therefore, the loss of energy in the perfectly inelastic collision is 32 Joules.