The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.030 kg and is moving along the x axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.055 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing.
(a) Find the final speed of puck A.
(b) Find the final speed of puck B.
im confused because i see two unknowns as to how to sole this please help thanks.
To solve this problem, you can use 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.
Let's start by finding the momentum of each puck before the collision. The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v).
Puck A:
Mass of puck A, m₁ = 0.030 kg
Velocity of puck A, v₁ = +5.5 m/s (positive since it is moving along the positive x-axis)
Momentum of puck A before collision, p₁ = m₁ * v₁
Puck B:
Mass of puck B, m₂ = 0.055 kg
Velocity of puck B before collision, v₂ = 0 m/s (since it is initially at rest)
Momentum of puck B before collision, p₂ = m₂ * v₂
Since puck B is initially at rest (v₂ = 0), its momentum before the collision, p₂, is zero. Therefore, the total momentum before the collision is equal to the momentum of puck A:
Total momentum before collision = Momentum of puck A before collision = p₁
Now, let's analyze the final momentum after the collision. The pucks fly apart with different angles, but the important thing to note is that momentum is a vector quantity. So, we need to consider both the magnitudes and directions of the final velocities of the pucks.
After the collision, let the final velocity of puck A be v₁f and the final velocity of puck B be v₂f.
The momentum of puck A after the collision, p₁f, can be calculated as:
p₁f = m₁ * v₁f
The momentum of puck B after the collision, p₂f, can be calculated as:
p₂f = m₂ * v₂f
According to the conservation of momentum principle, the total momentum after the collision is equal to the total momentum before the collision:
Total momentum after collision = Momentum of puck A after collision + Momentum of puck B after collision
Equating the total momentum before and after the collision:
p₁ = p₁f + p₂f
m₁ * v₁ = m₁ * v₁f + m₂ * v₂f
Now, we have two equations with two unknowns (v₁f and v₂f). We can solve these equations simultaneously to find the final velocities of the pucks.
Remember that the angles at which the pucks fly apart are not directly useful in solving this problem. You need to consider the magnitudes and directions of the velocities (speeds) of the pucks after the collision.