A 0.300 kg air-track glider moving at 2.20 m/s bumps into a 0.800 kg glider at rest.
a.) Find the total kinetic energy after collision if the collision is elastic.
b.) Find the total kinetic energy after collision if the collision is completely inelastic.
.3 * 2.2 = .3 u + .8 v
and if elastic
1/2(.3) (2.2)^2=1/2(.3)u^2+1/2(.8)v^2
and if inelastic (glued together)
u = v
.3*2.2 = 1.1 u
Ke = (1/2)(1.1)u^2
To find the total kinetic energy after the collision, we need to consider whether the collision is elastic or completely inelastic and apply the corresponding formulas.
a) If the collision is elastic, the total kinetic energy after the collision will be conserved. To calculate it, we can use the formula:
Total Kinetic Energy = (1/2) * m1 * v1^2 + (1/2) * m2 * v2^2
Where:
m1 = mass of the first glider = 0.300 kg
v1 = initial velocity of the first glider = 2.20 m/s
m2 = mass of the second glider = 0.800 kg
v2 = initial velocity of the second glider (at rest)
Substituting the values into the formula:
Total Kinetic Energy = (1/2) * 0.300 kg * (2.20 m/s)^2 + (1/2) * 0.800 kg * (0 m/s)^2
Total Kinetic Energy = (1/2) * 0.300 kg * 4.84 m^2/s^2 + (1/2) * 0.800 kg * 0 m^2/s^2
Total Kinetic Energy = 0.7312 J + 0 J
Total Kinetic Energy = 0.7312 J
Therefore, the total kinetic energy after the collision, if it is elastic, is 0.7312 J.
b) If the collision is completely inelastic, the two gliders will stick together after the collision, and their total kinetic energy will not be conserved. To calculate it, we can use the formula:
Total Kinetic Energy = (1/2) * (m1 + m2) * v^2
Where:
v = final velocity of the gliders after collision (since they stick together)
Substituting the values into the formula:
Total Kinetic Energy = (1/2) * (0.300 kg + 0.800 kg) * v^2
Total Kinetic Energy = (1/2) * 1.100 kg * v^2
To find the final velocity (v), we can use the principle of conservation of momentum:
Initial Momentum = Final Momentum
m1 * v1 + m2 * v2 = (m1 + m2) * v
(0.300 kg * 2.20 m/s) + (0.800 kg * 0 m/s) = (0.300 kg + 0.800 kg) * v
0.660 kg·m/s = 1.100 kg * v
v = 0.660 kg·m/s / 1.100 kg
v = 0.6 m/s
Substituting this velocity value back into the equation for total kinetic energy:
Total Kinetic Energy = (1/2) * 1.100 kg * (0.6 m/s)^2
Total Kinetic Energy = (1/2) * 1.100 kg * 0.36 m^2/s^2
Total Kinetic Energy = 0.198 J
Therefore, the total kinetic energy after the collision, if it is completely inelastic, is 0.198 J.