An elastic collision occurs between two pucks on an air-hockey table. Puck A has a mass of 0.025 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 0.060 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the following angles:
Puck A is 65 degrees above the x axis
Puck B is 37 degrees below the x axis
a) Find the final speed of Puck A
b) Find the final speed of Puck B
To find the final speed of Puck A and Puck B after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
a) Find the final speed of Puck A:
1. Calculate the initial momentum of Puck A:
Momentum = mass x velocity
Momentum_A_initial = 0.025 kg * 5.5 m/s = 0.1375 kg*m/s (in the positive x-direction)
2. Calculate the initial momentum of Puck B:
Since Puck B is initially at rest, its initial momentum is 0 kg*m/s.
3. Calculate the total initial momentum:
Total initial momentum = Momentum_A_initial + Momentum_B_initial
Total initial momentum = 0.1375 kg*m/s + 0 kg*m/s = 0.1375 kg*m/s
4. Calculate the total final momentum:
Since momentum is conserved in an elastic collision, the total final momentum is equal to the total initial momentum.
Total final momentum = Total initial momentum = 0.1375 kg*m/s
5. Calculate the x-component of the final momentum of Puck A:
Final momentum_A_x = Total final momentum * cos(angle_A)
Final momentum_A_x = 0.1375 kg*m/s * cos(65 degrees)
6. Calculate the y-component of the final momentum of Puck A:
Final momentum_A_y = Total final momentum * sin(angle_A)
Final momentum_A_y = 0.1375 kg*m/s * sin(65 degrees)
7. Calculate the final momentum of Puck A:
Final momentum_A = sqrt((Final momentum_A_x)^2 + (Final momentum_A_y)^2)
8. Calculate the final speed of Puck A:
Final speed_A = Final momentum_A / mass_A
Final speed_A = Final momentum_A / 0.025 kg
b) Find the final speed of Puck B:
9. Calculate the x-component of the final momentum of Puck B:
Final momentum_B_x = Total final momentum * cos(angle_B)
Final momentum_B_x = 0.1375 kg*m/s * cos(-37 degrees)
10. Calculate the y-component of the final momentum of Puck B:
Final momentum_B_y = Total final momentum * sin(angle_B)
Final momentum_B_y = 0.1375 kg*m/s * sin(-37 degrees)
11. Calculate the final momentum of Puck B:
Final momentum_B = sqrt((Final momentum_B_x)^2 + (Final momentum_B_y)^2)
12. Calculate the final speed of Puck B:
Final speed_B = Final momentum_B / mass_B
Final speed_B = Final momentum_B / 0.060 kg
By following these steps and plugging in the values given in the problem, you can find the final speed of Puck A and Puck B after the collision.