An 8.0 kg puck floating on an air table is travelling east at 15 cm/s. Coming the other way at 25 cm/s is a 2.0 kg puck on which is affixed a wad of bubble gum. The two slam head-on into each other and stick together. Find their velocity after the impact. How much kinetic energy was lost?
m1v1+m2v2 = v'(m1+m2)
This is the equation you must use so...
(8*15)+(2*(-25)) = v'(8+2)
The velocity for 25cm/s is negative because it's approaching the first puck in the opposite direction. Just find v' to find the velocity after impact.
Not sure for lost KE. Sorry.
To find the velocity of the pucks after the impact, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity:
momentum = mass × velocity
The momentum before the collision can be expressed as:
momentum_before = (mass1 × velocity1) + (mass2 × velocity2)
where mass1 = 8.0 kg, velocity1 = 15 cm/s, mass2 = 2.0 kg, and velocity2 = -25 cm/s (negative sign indicates opposite direction).
Calculating the momentum before the collision:
momentum_before = (8.0 kg × 15 cm/s) + (2.0 kg × -25 cm/s)
= 120 kg·cm/s - 50 kg·cm/s
= 70 kg·cm/s
Since both pucks stick together after the impact, they will have the same final velocity. Let's assume this final velocity is V. The momentum after the collision can be expressed as:
momentum_after = (total mass) × (final velocity)
The total mass would be the sum of the masses of the two pucks:
total mass = mass1 + mass2
Substituting the given values:
momentum_after = (8.0 kg + 2.0 kg) × V
= 10.0 kg × V
According to the law of conservation of momentum:
momentum_before = momentum_after
Solving for V:
70 kg·cm/s = 10.0 kg × V
V = (70 kg·cm/s) / 10.0 kg
= 7 cm/s
Therefore, the velocity of the pucks after the impact is 7 cm/s.
To calculate the kinetic energy lost during the collision, we need to determine the initial kinetic energy and the final kinetic energy.
The initial kinetic energy can be calculated using the formula:
initial kinetic energy = (1/2) × mass1 × (velocity1)^2 + (1/2) × mass2 × (velocity2)^2
Substituting the given values:
initial kinetic energy = (1/2) × 8.0 kg × (15 cm/s)^2 + (1/2) × 2.0 kg × (-25 cm/s)^2
= 600 J + 250 J
= 850 J
The final kinetic energy can be calculated using the formula:
final kinetic energy = (1/2) × (total mass) × (final velocity)^2
Substituting the calculated values:
final kinetic energy = (1/2) × 10.0 kg × (7 cm/s)^2
= 245 J
The kinetic energy lost during the collision is:
kinetic energy lost = initial kinetic energy - final kinetic energy
= 850 J - 245 J
= 605 J
Therefore, the kinetic energy lost during the collision is 605 J.