A 0.490 kg hockey puck, moving east with a speed of 5.80 m/s, has a head-on collision with a 0.870 kg puck initially at rest. Assume a perfectly elastic collision. (Let east be the +x direction.)
(a) What will be the speed of each object after the collision?
0.490 kg puck
0.870 kg puck
(b) What will be the direction of each puck after the collision?
A derivation of the equation for this situation can be found at
http://www.real-world-physics-problems.com/elastic-collision.html
To determine the speed of each object after the collision, we can use the principle of conservation of momentum. This principle states that the total momentum before the collision is equal to the total momentum after the collision in an isolated system.
Step 1: Find the initial momentum of each puck:
The momentum of an object is given by the equation:
momentum = mass x velocity
For the 0.490 kg puck:
momentum_before_collision_puck_1 = mass_puck_1 x velocity_puck_1 = (0.490 kg) x (5.80 m/s)
For the 0.870 kg puck:
momentum_before_collision_puck_2 = mass_puck_2 x velocity_puck_2 = (0.870 kg) x (0 m/s) [initially at rest]
Since the second puck is initially at rest, its initial momentum is zero.
Step 2: Find the total initial momentum:
total_initial_momentum = momentum_before_collision_puck_1 + momentum_before_collision_puck_2
Step 3: Apply conservation of momentum:
According to the conservation of momentum, the total momentum after the collision is equal to the total initial momentum.
Step 4: Find the speed of each object after the collision:
Since the collision is perfectly elastic, the kinetic energy is conserved as well. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The equation for kinetic energy is:
kinetic energy = (1/2) x mass x velocity^2
Since the initial kinetic energy of the second puck is zero (initially at rest), its final kinetic energy after the collision will also be zero.
Using the conservation of momentum and kinetic energy, we can solve for the final speed of each puck after the collision.
Step 5: Find the final velocity and direction of each puck:
Using the equations above, the final speeds can be determined.
The final velocity of the first puck can be found by solving the equation:
total_initial_momentum = (mass_puck_1 + mass_puck_2) x final_velocity_puck_1
Then, the final velocity of the second puck can be found by solving the equation:
momentum_before_collision_puck_1 - momentum_before_collision_puck_2 = mass_puck_1 x final_velocity_puck_1 - mass_puck_2 x final_velocity_puck_2
The direction of each puck after the collision can be determined by considering the conservation of momentum. Since the collision is head-on, the direction of the first puck after the collision will remain the same (east), and the direction of the second puck will change to the opposite direction (west).
By solving these equations, you can find the final speed and direction of each puck after the collision.