A body of mass 2kg moving with a velocity of 6m/s collides with a stationary object of mass 0.5kg if the two bodies move together after impact what is their common velocity and total force
To find the common velocity and total force of the two bodies after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision. The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = mv.
Before the collision:
Momentum of body 1: p1 = m1 * v1
Momentum of body 2: p2 = m2 * v2
After the collision:
Momentum of the combined system: p_final = (m1 + m2) * v_final
Using this equation, we can write:
m1 * v1 + m2 * v2 = (m1 + m2) * v_final
2. Conservation of kinetic energy:
The total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy (KE) of an object is given by half the product of its mass and the square of its velocity: KE = 0.5 * m * v^2.
Before the collision:
Kinetic energy of body 1: KE1 = 0.5 * m1 * v1^2
Kinetic energy of body 2 (since it is stationary, its initial kinetic energy is zero): KE2 = 0
After the collision:
Total kinetic energy of the combined system: KE_final = 0.5 * (m1 + m2) * v_final^2
Using this equation, we can write:
0.5 * m1 * v1^2 + 0 = 0.5 * (m1 + m2) * v_final^2
Now, let's substitute the given values into the equations:
m1 (mass of body 1) = 2 kg
v1 (velocity of body 1) = 6 m/s
m2 (mass of body 2) = 0.5 kg
Using these values, we can solve the equations to find the common velocity and total force:
1. Conservation of momentum equation:
2 kg * 6 m/s + 0.5 kg * 0 m/s = (2 kg + 0.5 kg) * v_final
12 kg m/s = 2.5 kg * v_final
v_final = 12 kg m/s / 2.5 kg
v_final = 4.8 m/s
Therefore, the common velocity after the collision is 4.8 m/s.
2. Conservation of kinetic energy equation:
0.5 * 2 kg * (6 m/s)^2 + 0 = 0.5 * (2 kg + 0.5 kg) * v_final^2
0.5 * 2 kg * 36 m^2/s^2 = 0.5 * 2.5 kg * v_final^2
36 kg m^2/s^2 = 1.25 kg * v_final^2
v_final^2 = 36 kg m^2/s^2 / 1.25 kg
v_final^2 = 28.8 m^2/s^2
v_final = √(28.8 m^2/s^2)
v_final ≈ 5.37 m/s
Therefore, the common velocity after the collision is approximately 5.37 m/s.
To find the total force, we need to use Newton's second law:
Force (F) = Change in momentum / Time
Since the time of collision is not given, we cannot determine the exact value of the total force without that information. However, we know that the force will be the same for both objects since they are in contact during the collision.