Two hockey pucks approach each other as shown in the figure below. Puck 1 has an initial speed of 22 m/s, and puck 2 has an initial speed of 14 m/s. They collide and stick together.
Find the components along x and y of the initial velocities of both particles.
v1xi = 19.1 m/s
v1yi = -11 m/s
v2ix = 0 m/s
v2iy = 14 m/s
I don't understand how to..
Find the final velocity of the two pucks after the collision and angle
What fraction of the initial kinetic energy is lost in the collision
Found the final velocity and angle..
just don't understand the initial KE part now
To find the final velocity of the two pucks after the collision, you can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. Since the two pucks stick together after the collision, they can be treated as a single combined object with a total mass equal to the sum of their individual masses.
Let's denote the final velocity of the combined pucks as vf and the total mass as m.
The total momentum before the collision is given by the sum of the individual momenta:
Initial momentum of puck 1: p1i = m1 * v1i
Initial momentum of puck 2: p2i = m2 * v2i
The total momentum after the collision is given by the momentum of the combined pucks:
Final momentum of combined pucks: pf = m * vf
According to the principle of conservation of momentum, p1i + p2i = pf.
Now, let's plug in the given values:
m1 = mass of puck 1
m2 = mass of puck 2
v1i = initial velocity of puck 1
v2i = initial velocity of puck 2
To find the fraction of initial kinetic energy lost in the collision, you need to compare the initial kinetic energy with the final kinetic energy of the combined pucks.
The initial kinetic energy is given by:
Initial kinetic energy = (1/2) * m1 * (v1i)^2 + (1/2) * m2 * (v2i)^2
The final kinetic energy is given by:
Final kinetic energy = (1/2) * m * (vf)^2
The fraction of initial kinetic energy lost in the collision can be calculated as the difference between the initial and final kinetic energies divided by the initial kinetic energy:
Fraction of energy lost = (Initial kinetic energy - Final kinetic energy) / Initial kinetic energy