A ball with a mass of #12 kg# moving at #7 m/s# hits a still ball with a mass of #24 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Question

A ball with a mass of #12 kg# moving at #7 m/s# hits a still ball with a mass of #24 kg#.  If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Lily Adams · Accepted Answer

#v_f= 3.5 m/s#
KE lost = #147J# By conservation of momentum: #p_i = p_f# #(12)(7) = (24)(v_f)# #v_f = 84/24 = 3.5m/s# By conservation of energy: #KE_i = KE_f + # heat energy lost #1/2 (12)(7)^2 = 1/2 (24)(3.5)^2 + KE_(lost)# #294 = 147 + KE_(lost)# #KE_(lost) = 147J#

Sebastian Acosta · Answer

undefined To find the velocity of the second ball after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Momentum before collision = Momentum after collision

(12 kg * 7 m/s) + (24 kg * 0 m/s) = (12 kg * 0 m/s) + (24 kg * v)

Solving for v, we get:

84 kg m/s = 24 kg * v

v = 84 kg m/s / 24 kg

v ≈ 3.5 m/s

To calculate the kinetic energy lost as heat in the collision, we first find the initial kinetic energy of the system before the collision and then subtract the final kinetic energy of the system after the collision.

Initial kinetic energy = (1/2) * mass * velocity^2
Initial kinetic energy = (1/2) * 12 kg * (7 m/s)^2

Final kinetic energy = (1/2) * mass * velocity^2
Final kinetic energy = (1/2) * 24 kg * (3.5 m/s)^2

Kinetic energy lost as heat = Initial kinetic energy - Final kinetic energy

Calculating the values:

Initial kinetic energy ≈ 294 J
Final kinetic energy ≈ 147 J

Kinetic energy lost as heat ≈ 294 J - 147 J ≈ 147 J