A bomb of mass 12 kilogram initially at rest ,explode into pieces of masses 4 kilogram and 8 kilogram. The speed of 8 kilogram is 6 meter per second. Then kinetic energy of 4 kilogram mass is
We can use conservation of momentum to find the speed of the 4 kg mass, and then use kinetic energy formula to find its kinetic energy.
Let v be the speed of the 4 kg mass after the explosion. Conservation of momentum gives:
12 kg * 0 m/s = 4 kg * v + 8 kg * 6 m/s
Simplifying:
0 = 4 kg * v + 48 kg*m/s
-48 kg*m/s = 4 kg * v
v = -12 m/s (note: the negative sign means the 4 kg mass is moving in the opposite direction to the 8 kg mass)
Now we can find the kinetic energy of the 4 kg mass using:
Kinetic energy = 1/2 * mass * velocity^2
Kinetic energy = 1/2 * 4 kg * (-12 m/s)^2
Kinetic energy = 288 J
Therefore, the kinetic energy of the 4 kg mass is 288 Joules.
To find the kinetic energy of the 4 kilogram mass, we can use the conservation of momentum.
The initial momentum before the explosion is zero since the bomb is initially at rest:
Initial momentum = 0 kg * m/s = 0 kg * m/s
After the explosion, the momentum should still be conserved. The momentum of each individual piece can be calculated using the equation p = mv, where p is momentum, m is mass, and v is velocity.
Let's assume the velocity of the 4 kilogram mass is v1.
From conservation of momentum:
Initial momentum = Final momentum
0 kg * m/s = 4 kg * v1 + 8 kg * 6 m/s
First, let's solve for v1:
0 kg * m/s = 4 kg * v1 + 8 kg * 6 m/s
0 kg * m/s = 4 kg * v1 + 48 kg * m/s
4 kg * v1 = -48 kg * m/s
v1 = -12 m/s
Now that we have the velocity of the 4 kilogram mass, we can calculate its kinetic energy using the equation KE = (1/2) * m * v^2, where KE is the kinetic energy, m is mass, and v is velocity.
KE = (1/2) * 4 kg * (-12 m/s)^2
KE = (1/2) * 4 kg * 144 m^2/s^2
KE = 288 J
Therefore, the kinetic energy of the 4 kilogram mass is 288 joules.