Alaskan moose can be as massive as 800 kg. Suppose two feuding moose, both of which have a mass of 800 kg, back away and then run toward each other. If one of them runs to the left with a speed of 6.0 m/s, and the other runs to the right with a speed of 8.0 m/s, what amount of kinetic energy will be dissipated after their inelastic collision?
You are probably supposed to assume that they stick together, with total momentum conserved. In that case, they end up traveling both at a speed V such that
1600*V = 800*8.0 - 800*6.0
V = 1.0 m/s
K.E. dissipated
= Initial KE - final KE
= (1/2)(2)*800*(8^2+6^2 - (1/2)1600*1^2
= 800*[100 - 1) = 79,200 J
To find the amount of kinetic energy dissipated after the inelastic collision, we first need to calculate the initial kinetic energy before the collision and then the final kinetic energy after the collision. The difference between them will give us the amount of kinetic energy dissipated.
1. Calculate the initial kinetic energy:
The kinetic energy (KE) of an object can be calculated using the formula KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
In this case, both moose have a mass of 800 kg. The first moose running left has a speed of 6.0 m/s, and the second moose running right has a speed of 8.0 m/s.
The initial kinetic energy of the first moose is KE1 = (1/2) * m * v1^2 = (1/2) * 800 kg * (6.0 m/s)^2 = 14,400 J
The initial kinetic energy of the second moose is KE2 = (1/2) * m * v2^2 = (1/2) * 800 kg * (8.0 m/s)^2 = 25,600 J
2. Calculate the final kinetic energy:
In an inelastic collision, the two objects stick together and move as one, conserving momentum but not kinetic energy. Therefore, after the collision, both moose will have the same final velocity.
To find the final velocity, we can use the conservation of momentum: m1 * v1 + m2 * v2 = (m1 + m2) * vf
Here, m1 and m2 are the masses of the moose, v1 and v2 are their initial velocities, and vf is their final velocity.
Since both moose have the same mass (800 kg) and opposite velocities, their total momentum before the collision is zero.
Thus, 800 kg * 6.0 m/s + 800 kg * (-8.0 m/s) = (800 kg + 800 kg) * vf
4800 kg * m/s - 6400 kg * m/s = 0
-1600 kg * m/s = 0
Therefore, the final velocity (vf) is 0.
The final kinetic energy is KEf = (1/2) * (m1 + m2) * vf^2 = (1/2) * 1600 kg * (0 m/s)^2 = 0 J
3. Calculate the amount of kinetic energy dissipated:
The difference between the initial kinetic energy (KE1 + KE2 = 14,400 J + 25,600 J = 40,000 J) and the final kinetic energy (0 J) gives us the amount of kinetic energy dissipated.
KEdissipated = 40,000 J - 0 J = 40,000 J
Therefore, the amount of kinetic energy dissipated after their inelastic collision is 40,000 Joules.