Answer:
The final speed of the second bicycle is (v·√2)/2
Explanation:
The mass of the given bicycle = m
The amount of work required to move the bicycle from rest to speed v = 50 J
The final speed of the first bicycle = v
The mass of the second bicycle = 2m
Therefore, from conservation of energy, we have;
Work required by the first bicycle = Kinetic energy gained by the bicycle
The kinetic energy = 1/2·m·v²
∴ Energy required by the first bicycle = 50 J = 1/2·m·v²
Given that the same amount of work is performed on the second bicycle, we have;
Work performed on the second bicycle = 50 J = kinetic energy of second bicycle = 1/2·(2·m)·v₂²
Also, given that 50 J = 1/2·m·v², we have;
Work performed on the second bicycle = 50 J = 1/2·m·v²= 1/2·(2·m)·v₂²
1/2·m·v²= 1/2·(2·m)·v₂²
m·v² = 2·m·v₂²
v² = 2·v₂²
v₂ = √(v²/2) = v/√2 = (v·√2)/2
v₂ = (v·√2)/2
The final speed of the second bicycle = v₂ = (v·√2)/2.
