Answer:
The decrease in Kinetic energy is 0.0107 Joules
Explanation:
Given
Mass of grasshoppers
Let m1 = Mass of grasshopper 1
Let m2 = Mass of grasshopper 2
Let u1 = initial speed of grasshopper 1
Let u2 = initial speed of grasshopper 2
m1 = 250g = 0.25kg
m2 = 130g = 0.13kg
u1 = 15cm/s = 0.15m/s
u2 = 65cm/s = 0.65m/s
First, we calculate the final velocity of the grasshoppers after collision using conservation of momentum.
Using
m1u1 + m2u2 = (m1 + m2) * v
Where v = final velocity
By substituton
0.25 * 0.15 + 0.13 * 0.65 = (0.25 + 0.13) * v
0.0375 + 0.0845 = 380v
0.122 = 0.38v
Make v the subject of formula
v = 0.122/0.38
v = 0.321 m/s
Calculating the Kinetic energies before and after impact.
Before collision;
KE = ½m1u1²+ ½m2u2²
KE = ½(m1u1² + m2u2²)
By substituton;
KE = ½(0.25 * 0.15² + 0.13 * 0.65²)
KE = 0.030275J
After collision:
KE = ½(m1+m2)v²
KE = ½(0.25 + 0.13) * 0.321²
KE = 0.01957779 J
Change in kinetic energy = ∆KE
∆KE = 0.030275J - 0.01957779J
∆KE = 0.01069721J
∆KE = 0.0107 J --- Approximately
Hence the decrease in Kinetic energy is 0.0107 Joules
