Search: The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.029 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 0.049 kg and is initially at rest. After the collision, the two pucks fly apart with the angles shown in the drawing.
To solve this problem, we can use the principle of conservation of momentum and the law of conservation of kinetic energy.
Step 1: Calculate the initial momentum of Puck A
The initial momentum of Puck A is given by the product of its mass and velocity:
Initial momentum of Puck A = mass of Puck A * velocity of Puck A
= 0.029 kg * +5.5 m/s
= +0.1595 kg*m/s (The positive sign indicates the direction along the x-axis)
Step 2: Calculate the initial momentum of Puck B
Since Puck B is initially at rest, its initial momentum is zero:
Initial momentum of Puck B = 0 kg*m/s
Step 3: Calculate the total initial momentum
The total initial momentum is the sum of the initial momenta of Puck A and Puck B:
Total initial momentum = Initial momentum of Puck A + Initial momentum of Puck B
= +0.1595 kg*m/s + 0 kg*m/s
= +0.1595 kg*m/s
Step 4: Apply the principle of conservation of momentum
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Step 5: Calculate the final momentum of Puck A
Let the magnitude of the final velocity of Puck A be vA and the angle it makes with the x-axis be θA. The final momentum of Puck A can be written as:
Final momentum of Puck A = mass of Puck A * velocity of Puck A after collision
Final momentum of Puck A = 0.029 kg * vA
Step 6: Calculate the final momentum of Puck B
Let the magnitude of the final velocity of Puck B be vB and the angle it makes with the x-axis be θB. The final momentum of Puck B can be written as:
Final momentum of Puck B = mass of Puck B * velocity of Puck B after collision
Final momentum of Puck B = 0.049 kg * vB
Step 7: Apply the principle of conservation of momentum
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can write the following equation:
Total initial momentum = Total final momentum
+0.1595 kg*m/s = 0.029 kg * vA + 0.049 kg * vB
Step 8: Apply the law of conservation of kinetic energy
According to the law of conservation of kinetic energy, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Since Puck B is initially at rest, its initial kinetic energy is zero. Therefore, we can write the following equation:
(mass of Puck A * (velocity of Puck A)^2) / 2 = (mass of Puck A * (velocity of Puck A after collision)^2) / 2 + (mass of Puck B * (velocity of Puck B after collision)^2) / 2
Step 9: Solve the equations
Solving the equations from steps 7 and 8 will give you the final velocities (vA and vB) of the pucks after the collision.
Please note that the angles at which the pucks fly apart are not mentioned in the provided information. Therefore, we cannot determine the angles without additional information.
To solve this problem, we need to apply the laws of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
The formula for momentum is:
momentum = mass * velocity
Before the collision:
momentum_A_before = mass_A * velocity_A
momentum_B_before = mass_B * velocity_B_before, where velocity_B_before is the initial velocity of puck B, which is 0 m/s.
After the collision:
momentum_A_after = mass_A * velocity_A_after
momentum_B_after = mass_B * velocity_B_after
According to conservation of momentum:
momentum_A_before + momentum_B_before = momentum_A_after + momentum_B_after
Since momentum_B_before is zero, the equation simplifies to:
momentum_A_before = momentum_A_after + momentum_B_after
2. Conservation of kinetic energy states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The formula for kinetic energy is:
kinetic energy = 0.5 * mass * velocity^2
Before the collision:
kinetic_energy_A_before = 0.5 * mass_A * velocity_A^2
kinetic_energy_B_before = 0 (as puck B is initially at rest)
After the collision:
According to conservation of kinetic energy:
kinetic_energy_A_before = kinetic_energy_A_after + kinetic_energy_B_after
Since kinetic_energy_B_before is zero, the equation simplifies to:
kinetic_energy_A_before = kinetic_energy_A_after + kinetic_energy_B_after
To solve for the unknown variables (velocity_A_after, velocity_B_after), we need to use the given information about the masses and initial velocities of the pucks, as well as the angles at which they fly apart.