Two pucks collide on an air hockey table. Puck A has a mass of 17.0 g and is initially traveling in the +x direction at 7.00 m/s. Puck B has a mass of 51.0 g and is initially at rest. After the pucks collide, puck A moves away at an angle of 52.0 deg above the +x axis, while puck B travels at an angle of 28.0 deg below the +x axis.
A) Calculate puck A's final speed.
B) Calculate puck B's final speed.
C) What fraction of kinetic energy was lost in this collision?
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy. Let's break down the problem step by step:
Step 1: Find the final velocities of the pucks in the x and y directions.
Step 2: Calculate the final speeds of the pucks using the x and y components.
Step 3: Calculate the initial and final kinetic energies.
Step 4: Determine the fraction of kinetic energy lost.
Let's begin with step 1:
Step 1: Find the final velocities of the pucks in the x and y directions.
Puck A's initial velocity (vA1) in the x-direction is 7.00 m/s. Puck B is initially at rest, so its initial velocity (vB1) in the x-direction is 0.
After the collision, puck A moves away at an angle of 52.0 degrees above the +x-axis, while puck B moves at an angle of 28.0 degrees below the +x-axis.
Using trigonometry, we can find the x and y components of the final velocities for each puck.
For puck A:
vA1x = vA1 * cos(angleA) = 7.00 m/s * cos(52.0 degrees)
vA1y = vA1 * sin(angleA) = 7.00 m/s * sin(52.0 degrees)
For puck B:
vB1x = 0
vB1y = -vB1 * sin(angleB) = -0 * sin(28.0 degrees)
Step 2: Calculate the final speeds of the pucks using the x and y components.
To find the final speed (vA2 or vB2) for each puck, we can use the Pythagorean theorem:
vA2 = sqrt(vA2x^2 + vA2y^2)
vB2 = sqrt(vB2x^2 + vB2y^2)
Step 3: Calculate the initial and final kinetic energies.
The kinetic energy of an object can be calculated using the formula:
KE = 1/2 * m * v^2
For puck A:
Initial kinetic energy (KEA1) = 1/2 * mA * vA1^2
Final kinetic energy (KEA2) = 1/2 * mA * vA2^2
For puck B:
Initial kinetic energy (KEB1) = 1/2 * mB * vB1^2
Final kinetic energy (KEB2) = 1/2 * mB * vB2^2
Step 4: Determine the fraction of kinetic energy lost.
The fraction of kinetic energy lost in a collision can be calculated using the formula:
Fraction of kinetic energy lost = (Initial kinetic energy - Final kinetic energy) / Initial kinetic energy