Hockey puck A initially travels at v(initial) = 6.2 m/s in the horizontal direction (East) on a smooth horizontal ice before striking hockey puck B which is initially at rest, off-center. After the collision, A is deflected at θ = 23 degrees 'above' its original direction, while puck B is deflected at α = 30.7 degrees 'below' the original direction of puck A. The pucks have the same mass.
What is the speed of puck A after the collision?
What percentage of the initial kinetic energy of the system is converted to other forms (i.e. dissipated) during the collision? (Note: you will need to determine the final speed of the other puck B first.)
To find the speed of puck A after the collision, we can use the conservation of momentum and the conservation of kinetic energy.
Step 1: Find the final speed of puck B.
Since the pucks have the same mass and puck A initially travels at 6.2 m/s and deflects at an angle of 23 degrees 'above' its original direction, we can use trigonometry to calculate the horizontal and vertical components of its velocity after the collision.
The horizontal component is given by: vx = v * cos(23)
The vertical component is given by: vy = v * sin(23)
Since puck B is initially at rest and deflects at an angle of 30.7 degrees 'below' the original direction of puck A, its velocity components after the collision can be calculated using trigonometry as well.
The horizontal component is given by: bx = 0
The vertical component is given by: by = v * sin(30.7)
Since momentum is conserved, the sum of the x-components of momentum before the collision is equal to the sum of the x-components of momentum after the collision.
m * v(initial) = m * vx(A) + m * bx(B)
6.2 = vx(A)
Similarly, the sum of the y-components of momentum before the collision is equal to the sum of the y-components of momentum after the collision.
0 = vy(A) + by(B)
0 = v * sin(23) - v * sin(30.7)
Solve these two equations simultaneously to find the final vertical component of puck A's velocity.
Step 2: Calculate the final speed of puck A.
Using the final horizontal and vertical components of puck A's velocity, we can apply the Pythagorean theorem to find its final speed.
v(final)^2 = vx(A)^2 + vy(A)^2
Step 3: Calculate the percentage of dissipated energy.
The initial kinetic energy of the system can be found using the equation:
KE(initial) = 0.5 * m * v(initial)^2
The final kinetic energy of the system can be found using the equation:
KE(final) = 0.5 * m * v(final)^2
The percentage of dissipated energy can then be calculated by:
Percentage = (KE(initial) - KE(final))/ KE(initial) * 100.
By following these steps, you should be able to find the speed of puck A after the collision and the percentage of the initial kinetic energy that is converted to other forms.