A sphere of mass 0.4kg moving on a smooth billiard table hit a stationary sphere of mass 0.8kg and was brought to rest. Calculate the velocity at which the second sphere tends to move and loss in K.E energy
momentum is conserved,
.4V=.8v'
v'=1/2 V
new KE= 1/2 .8 (v'^2)1/2*.8*(1/2 v)^2
= 1/2*.8*1/4* v^2
loss of KE= old ke-new ke
= .4/2 v^2-.1/8 v^2
To calculate the velocity at which the second sphere tends to move, 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 if no external forces are present.
The momentum of an object is defined as the product of its mass and velocity, given by the formula: momentum = mass * velocity.
Let's denote the velocity of the first sphere (initially moving) as V1, the velocity of the second sphere (initially at rest) as V2, the mass of the first sphere as m1, and the mass of the second sphere as m2.
Before the collision, the total momentum is given by:
Initial momentum = (m1 * V1) + (m2 * 0) (since the second sphere is initially at rest)
After the collision, the first sphere is brought to rest, so its velocity becomes 0, and the second sphere starts moving with a velocity (V2).
Final momentum = (0 * m1) + (m2 * V2)
According to the principle of conservation of momentum:
(m1 * V1) + (m2 * 0) = 0 + (m2 * V2)
Simplifying the equation, we have:
m1 * V1 = m2 * V2
Now, we can plug in the given values:
m1 = 0.4 kg (mass of the first sphere)
V1 = unknown (velocity of the first sphere)
m2 = 0.8 kg (mass of the second sphere)
V2 = unknown (velocity of the second sphere)
0.4 * V1 = 0.8 * V2
Since the first sphere comes to rest, V1 = 0. The equation becomes:
0 = 0.8 * V2
Because any number multiplied by zero is zero, we conclude that V2 = 0 m/s. The second sphere tends to move with a velocity of 0 m/s.
Now, let's calculate the loss in kinetic energy (K.E.) during the collision. The initial kinetic energy is given by:
Initial K.E. = 0.5 * m1 * (V1^2) + 0.5 * m2 * (0^2) (since the second sphere is at rest)
After the collision, both spheres are at rest, so the final kinetic energy is 0.
The loss in kinetic energy is given by:
Loss in K.E. = Initial K.E. - Final K.E.
Loss in K.E. = 0.5 * m1 * (V1^2) + 0.5 * m2 * (0^2) - 0
Since V1 is 0, the equation becomes:
Loss in K.E. = 0.5 * m1 * (0^2) + 0.5 * m2 * (0^2)
Any number multiplied by zero is zero, so the loss in K.E. is 0.
Therefore, the velocity at which the second sphere tends to move is 0 m/s, and there is no loss in kinetic energy during the collision.