Answer:
20J
Explanation:
Using conservation law of momentum;
since the bodies were at rest, their initial momentum is zero
0 = M1Vx + M2Vy
- M1Vx = M2Vy where Vx is the final velocity of x after the spring has been release and Vy is final velocity of y and M1 and M2 are the masses of x and y
also M1 = 2/5 M2
substitute M1 into the the equation above
-2/5 M2Vx = M2Vy
cancel M2 on both side
-2/5Vx = Vy
comparing the kinetic energy of both x and y
for x K.E = 1/2 M1 Vx²
and y K.E = 1/2M2 Vy²
substitute for M1 = 2/5 M2
K.Ex = 1/2 × 2/5 M2 Vx²
divide K.Ex / K.Ey = (1/2 × 2/5 M2 Vx²) / 1/2 M2 Vy²
cancel the common terms
K.Ex / K.Ey = (2/5 Vx²) / Vy²
substitute -2/5Vx for Vy
(2/5 Vx²) / ( -2/5 Vx)² = (2/5 Vx²) / ( 4/25 Vx²)
cancel Vx²
(2/5) / (4/25) = 2/5 ÷ 4/25 = 2/5 × 25/4 = 5/2
the ratio of x and y kinetic energy is 5:2
since the kinetic energy of x is 50
50 : 20 = 5 : 2 if 10 is used to divide both sides
the kinetic energy of y = 20 J
