suppose a ball having 2 kilogram mass is closed in tube having 4 kilogram mass. what will be the velocity of 2 kilogram ball if we shake this tube side by side and this ball bounce back and rolling at the rate of .03 centimeter/second.
To calculate the velocity of the 2-kilogram ball, we need to consider the principle of conservation of momentum. When the tube is shaken side by side, the ball will experience a force that causes it to move. The force transfers momentum from the tube to the ball.
First, we need to determine the initial momentum of the system (tube + ball) before the ball starts moving. Momentum (p) is calculated by multiplying the mass (m) and velocity (v): p = m * v.
The initial momentum of the system will be the sum of the momenta of the tube and the ball, which can be expressed as follows:
Initial momentum = (mass of the tube * velocity of the tube) + (mass of the ball * velocity of the ball)
Given that the mass of the tube is 4 kilograms and the mass of the ball is 2 kilograms, and assuming that the tube is stationary before shaking, the initial momentum simplifies to:
Initial momentum = (4 kg * 0 m/s) + (2 kg * 0 m/s) = 0 kg∙m/s
Since the initial momentum is zero, the final momentum of the system after the ball starts moving will also be zero, as momentum is conserved.
The ball will move in the opposite direction to the tube with a certain velocity, which we need to determine. Let's represent the velocity of the ball as V.
Finally, we'll use conservation of momentum again to calculate the velocity of the ball. The equation can be expressed as:
(mass of the tube * velocity of the tube) + (mass of the ball * velocity of the ball) = 0
(4 kg * 0 m/s) + (2 kg * V) = 0
0 + 2V = 0
Therefore, the velocity of the 2-kilogram ball will be 0 m/s, meaning it will come to a complete stop.
However, please note that the information about the ball bouncing back and rolling at a rate of 0.03 centimeters/second is contradictory to the previous conditions provided regarding the ball's velocity. Please clarify if you would like me to consider this additional information when calculating the velocity.