A ball of mass 0.05 moving at 10m per seconds collides with another ball of equal mass at rest if two balls move off together after the impact calculate the common velocity
To calculate the common velocity of the two balls after the collision, we can use the principle of conservation of momentum.
The equation for conservation of momentum is:
(m1 * v1) + (m2 * v2) = (m1 + m2) * vf
Where:
m1 = mass of the first ball (0.05 kg)
v1 = velocity of the first ball before collision (10 m/s)
m2 = mass of the second ball (0.05 kg)
v2 = velocity of the second ball before collision (0 m/s)
vf = common velocity of both balls after collision
Plugging in the given values:
(0.05 kg * 10 m/s) + (0.05 kg * 0 m/s) = (0.05 kg + 0.05 kg) * vf
(0.5 kg m/s) + 0 kg m/s = 0.1 kg * vf
0.5 kg m/s = 0.1 kg * vf
Dividing both sides by 0.1 kg gives us:
0.5 kg m/s / (0.1 kg) = vf
vf = 5 m/s
Therefore, the common velocity of the two balls after the collision is 5 m/s.
To calculate the common velocity of the two balls after the impact, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object can be calculated by multiplying its mass by its velocity. In this case, the mass of each ball is 0.05 kg.
Before the collision, the first ball has a momentum of:
Momentum1 = mass1 * velocity1 = 0.05 kg * 10 m/s
Since the second ball is at rest, its momentum is zero.
The total momentum before the collision is given by the sum of the individual momenta:
Total momentum before collision = Momentum1 + Momentum2 = Momentum1 + 0
After the collision, the two balls move off together with a common velocity, which we'll call "v". The total momentum after the collision is given by the sum of the individual momenta of the balls:
Total momentum after collision = (mass1 + mass2) * v
Since the balls have equal mass, the mass of each ball is 0.05 kg, and there are two balls:
Total momentum after collision = (0.05 kg + 0.05 kg) * v = (0.1 kg) * v
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Total momentum before collision = Total momentum after collision
Momentum1 + 0 = (0.1 kg) * v
0.05 kg * 10 m/s = (0.1 kg) * v
Now, we can solve for the common velocity "v":
v = (0.05 kg * 10 m/s) / (0.1 kg)
v = 0.5 m/s
Therefore, the common velocity of the two balls after the impact is 0.5 m/s.
m1 = mass of ball 1 = 0.05kg
m2 = mass of ball 2 = 0.05kg
u = Initial velocity = 10m/s
v = Final velocity
Use the conservation of momentum:
Initial momentum = Final momentum
=> m1*u = (m1+m2)*v
=> 0.05*10 = (0.05+0.05)v
=> 0.5 = 0.1v
=> v = 5m/s