Question

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 1

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

    $K_i = \dfrac{1}{2}m_1v_1^2 + \dfrac{1}{2}m_2v_2^2$

    $K_i = \dfrac{1}{2}\times 8 \times 5.5^2 + \dfrac{1}{2}\times 5.75 \times 6^2$

            K_i = 224.5 J

final kinetic energy

                 =$\dfrac{1}{2}(m_1+m_2)V^2$

                 =$\dfrac{1}{2}(8+5.57)(-0.69)^2$

              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.