An American football game has been canceled because of bad weather in Cleveland, and two retired players are sliding like children on a frictionless ice-covered parking lot. William 'Refrigerator' Perry, mass 162 kg, is gliding to the right at 7.73 m/s, and Doug Flutie, mass 81.0 kg, is gliding to the left at 10.5 m/s along the same line. When they meet, they grab each other and hang on.

Question

An American football game has been canceled because of bad weather in Cleveland, and two retired players are sliding like children on a frictionless ice-covered parking lot. William 'Refrigerator' Perry, mass 162 kg, is gliding to the right at 7.73 m/s, and Doug Flutie, mass 81.0 kg, is gliding to the left at 10.5 m/s along the same line. When they meet, they grab each other and hang on.

(a) What is their velocity immediately thereafter?
(b) What fraction of their original kinetic energy is still mechanical energy after their collision?
(c) The athletes had so much fun that they repeat the collision with the same original velocities, this time moving along parallel lines 1.07 m apart. At closest approach they lock arms and start rotating about their common center of mass. Model the men as particles and their arms as a cord that does not stretch. Find the velocity of their center of mass.
(d) Find their angular speed.
(e) What fraction of their original kinetic energy is still mechanical energy after they link arms?

for part a do you have to use rotational kinetic energy or is it just translational? the numbers i keep getting are way off

Answer 1

Part A is linear momentum conservation.

Answer 2

i see what i was doing wrong now. i didn't take into account that they're going in opposite directions

Answer 3

For part (a), we can assume that the two players form a system with zero net external force acting on them. Therefore, according to the principle of conservation of linear momentum, the total momentum of the system before the collision is equal to the total momentum after the collision.

Let's denote William Perry's initial velocity as v1 (7.73 m/s to the right) and Doug Flutie's initial velocity as v2 (-10.5 m/s to the left).

The momentum of William Perry before the collision (P1) is given by:
P1 = mass1 * v1
P1 = 162 kg * 7.73 m/s

The momentum of Doug Flutie before the collision (P2) is given by:
P2 = mass2 * v2
P2 = 81.0 kg * (-10.5 m/s)

The total momentum of the system before the collision (P_initial) is the sum of P1 and P2:
P_initial = P1 + P2

Now, since William Perry and Doug Flutie grab each other and hang on, they become a single entity after the collision, meaning their final velocity will be the same.

Let the final velocity of the combined system be v_final. Since they grab each other and hang on, their masses add up:
Total mass = mass1 + mass2

Using the principle of conservation of momentum, the total momentum of the system after the collision (P_final) is:
P_final = Total mass * v_final

Now, equating the initial and final momenta:
P_initial = P_final

Substituting the expressions we derived above:
P1 + P2 = (mass1 + mass2) * v_final

Now solve for v_final.

Note: In this scenario, where the two players grab each other and hang on, the rotational kinetic energy is not required to determine their velocity immediately after the collision.