A 2.0-kg object moving at 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision.

20 J

Explanation:

From the question, since there is a lost in kinetic energy, Then the collision is an inelastic collision.

m'u'+mu = V (m+m') ... Equation 1

Where m' = mass of the moving object, m = mass of the stick, u' = initial velocity of the moving object, initial velocity of the stick, V = common velocity after collision.

make V the subject of the equation above

V = (m'u'+mu) / (m+m') ... Equation 2

Given: m' = 2 kg, m = 8 kg, u' = 5 m/s, u = 0 m/s (at rest).

Substitute into equation 2

V = [ (2*5) + (8*0) ] / (2+8)

V = 10/10

V = 1 m/s.

Lost in kinetic energy = Total kinetic energy before collision - total kinetic energy after collision

Total kinetic energy before collision = 1/2 (2) (5²) = 25 J

Total kinetic energy after collision = 1/2 (2) (1²) + 1/2 (8) (1²) = 1+4 = 5 J

Lost in kinetic energy = 25-5 = 20 J