a pair of identical pucks move towards either other on a frictionless surface with equal speeds, the pucks move apart after colliding. during interaction 3/4 of energy is lost. what is the ratio (momentum of before collision)/(momentum of after the collision)?
One.
If there are no external forces on the two puck system, there is no change in the total momentum. (Even if it approaches 0/0 )
Well, isn't that an extraordinary collision! It seems like those pucks had a real disagreement and decided to go their separate ways. Now, let's tackle that ratio of momentum, shall we?
Firstly, let's assume the initial momentum of the two identical pucks moving towards each other is "P." Since momentum is conserved in this frictionless system, the total momentum before the collision is 2P.
Now, during the interaction, 3/4 of the total energy is lost. But remember, momentum and energy are two different things, like cake and icing. They may hang out together, but they have separate identities.
So, the energy loss doesn't directly affect momentum. Therefore, the momentum ratio can be calculated as follows:
Momentum after the collision = 2P - 3/4 * 2P = 2P - 3/2P = 1/2P
Now, to find the ratio of the momentum before the collision to the momentum after the collision, we divide:
(Momentum before collision) / (Momentum after collision) = (2P) / (1/2P) = 4
Voila! The ratio of momentum before the collision to the momentum after the collision is 4. It seems like those pucks went from being a dynamic duo to "four"-ever alone!
To answer this question, we need to consider the conservation of momentum and energy.
Let's assume the mass of each puck is 'm' and the initial velocity of each puck is 'v'.
Before the collision:
The momentum of each puck before the collision is given by:
Momentum = mass * velocity = m * v
So, the total momentum of both pucks is:
Total momentum before collision = (m * v) + (m * v) = 2m * v
During the collision, 3/4 of the energy is lost. In other words, only 1/4 of the initial energy remains. Since kinetic energy is directly proportional to the square of velocity, we can calculate the velocity after the collision as follows:
Velocity after collision = square root of (1/4) * (initial velocity)^2
= (1/2) * (initial velocity)
After the collision:
The momentum of each puck after the collision is given by:
Momentum = mass * velocity = m * (1/2 * v)
So, the total momentum of both pucks after the collision is:
Total momentum after collision = (m * 1/2 * v) + (m * 1/2 * v) = m * v
The ratio of the momentum before the collision to the momentum after the collision is:
(momentum before collision) / (momentum after collision) = (2m * v) / (m * v) = 2/1 = 2
Therefore, the ratio of the momentum before collision to the momentum after collision is 2.
To find the ratio of momentum before the collision to the momentum after the collision, we need to understand the principles of conservation of momentum.
Conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, since the surface is frictionless and no external forces are mentioned, we can assume it is an isolated system.
Let's denote the momentum before the collision as P_i and the momentum after the collision as P_f.
Since the two pucks are identical and have equal initial speeds, their initial momentum is the same. Therefore, we can say that the momentum before the collision is equal for both pucks, i.e., P_i1 = P_i2.
Given that 3/4 (or 75%) of the energy is lost during the interaction, we can assume that the pucks come to rest after the collision. As a result, the final momentum of each puck is zero. Therefore, we can say that the momentum after the collision is zero for each puck, i.e., P_f1 = P_f2 = 0.
Now, let's calculate the ratio of momentum before the collision to the momentum after the collision:
Ratio = (P_i1 + P_i2) / (P_f1 + P_f2)
Since P_i1 = P_i2 and P_f1 = P_f2 = 0, we can simplify the equation:
Ratio = 2P_i / 0
Any number divided by zero is undefined, so we cannot determine the ratio in this scenario.
Therefore, the ratio of momentum before the collision to the momentum after the collision is undefined.