A stationary mass explodes in to two parts of masses 0.4 Kg and 4 Kg . if the larger mass has a kinetic energy of 100J ,what is the kinetic energy of the small mass ?
2 v^2 = 100
v = 10/sqrt 2 = speed of 2 kg mass
4 (10/sqrt 2) = .4 V
V = 100/sqrt 2 speed of small mass
(1/2)(.4)(10,000/2) = 1,000 = Ke of little mass
To solve this problem, we can use the principle of conservation of momentum.
The initial momentum of the system is zero since the mass is stationary before the explosion. The final momentum of the system should also be zero because there are no external forces acting on the system.
We can use the equation for momentum:
Initial momentum = Final momentum
Since the initial momentum is zero and the two masses are moving in opposite directions after the explosion, their momenta should differ in sign. Let's denote the final velocities of the small and large masses as v1 and v2, respectively.
Therefore, the equation for momentum becomes:
0 = (0.4 kg)(v1) + (-4 kg)(v2)
Simplifying the equation:
0 = 0.4v1 - 4v2
Next, we can use the equation for kinetic energy:
K.E. = (1/2)mv^2
Given that the kinetic energy of the larger mass is 100 J, we can write:
100 J = (1/2)(4 kg)(v2)^2
Simplifying the equation:
200 = (v2)^2
Taking the square root of both sides:
√200 = v2
√200 = 10√2
Now we can substitute this value back into the momentum equation:
0 = 0.4v1 - 4(10√2)
0 = 0.4v1 - 40√2
0.4v1 = 40√2
v1 = (40√2) / 0.4
v1 = 100√2
Next, we can calculate the kinetic energy of the smaller mass using the equation for kinetic energy:
K.E. = (1/2)mv^2
K.E. = (1/2)(0.4 kg)(100√2)^2
K.E. = (1/2)(0.4 kg)(20000)
K.E. = 4000 J
Therefore, the kinetic energy of the small mass is 4000 J.
To solve this problem, we need to use the law of conservation of momentum. According to this law, the total momentum before the explosion will be equal to the total momentum after the explosion.
Before the explosion, the mass was stationary, which means its momentum was zero. After the explosion, the total momentum will still be zero because there are no external forces acting on the system. Therefore, the momentum before and after the explosion is zero.
The momentum of an object can be calculated by multiplying its mass by its velocity. So, we have the equation:
(mass1 * velocity1) + (mass2 * velocity2) = 0
Here, mass1 is the mass of the small part (0.4 kg), velocity1 is the velocity of the small part, mass2 is the mass of the large part (4 kg), and velocity2 is the velocity of the large part.
Since we know the velocity of the large part is zero (as it is stationary after the explosion), we can rewrite the equation as:
(0.4 kg * velocity1) + (4 kg * 0) = 0
Simplifying this equation, we get:
0.4 kg * velocity1 = 0
To solve for the velocity of the small part, we divide both sides of the equation by 0.4 kg:
velocity1 = 0 / 0.4 kg = 0 m/s
Now we can calculate the kinetic energy of the small mass using the formula:
Kinetic energy (KE) = (1/2) * mass * velocity^2
Substituting the values, we have:
KE = (1/2) * 0.4 kg * (0 m/s)^2
Simplifying, we find:
KE = (1/2) * 0.4 kg * 0
KE = 0 J
Therefore, the kinetic energy of the small mass is 0 J.