Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. one of them, of mass 8.00kg , is sliding to the left at 5.50m/s , while the other, of mass 5.75kg , is slipping to the right at 6.00m/s . they hold fast to each other after they collide.

1. find the magnitude of the velocity of these free-spirited otters right after they collide.
2. find the direction of the velocity of these free-spirited otters right after they collide. (right or left)
3. how much mechanical energy dissipates during this play?

Answer

given,

mass of block (m₁)= 8 kg

mass of other block (m₂) = 5.75

velocity of first object (v₁) = 5.5 m/s

velocity of second object (v₂) = 6 m/s

a) total momentum before collision = total momentum after collision

  m₂v₂ - m₁ v₁ = (m₁ + m₂) V

  5.75 x 6 - 8 x 5.5 = (5.75 + 8 ) V

    V = - 0.69 m/s

b) negative sign shows the direction motion of object after collision toward left.

c) Initial kinetic energy

            K_i = 224.5 J

final kinetic energy

                 =

                 =

              K_f = 3.23 J

loss in mechanical energy

 Δ KE = 3.23 - 224.5

Δ KE = -218.1 J

negative sign shows loss of mechanical energy.

answer: 2×10^-2kg

explanation: density= mass per volume

vol=mass/density

converting to s.i units we have;

3÷1000kg = 0.003

1.5÷100m = 0.15

0.003/0.15 = 0.02kg