Answer:
The speed should be reduced by 1/√2 or 0.707 times
Explanation:
The relationship between the kinetic energy, mass and velocity can be represented by the following equation:
K.E = ½m.v²
In this equation, the mass is inversely proportional to the square of the velocity or speed. This means that as the mass increases, the speed reduces by × 2.
Let; initial mass = m1
Final mass = m2
Initial velocity = v1
Final velocity = v2
According to the question, if the mass of the body is doubled i.e. m2 = 2m
½m1v1² = ½m2v2²
½ × m × v1² = ½ × 2m × v2²
Multiply both sides by 2
(½ × m × v1²)2 = (½ × 2m × v2²)2
m × v1² = 2m × v2²
Divide both sides by m
v1² = 2v2²
Divide both sides by 2
v1²/2= v2²
Square root both sides
√v1²/2= √v2²
v1/√2 = v2
v2 = 1/√2 v1
This shows that to maintain the same kinetic energy if the mass is doubled, the speed should be reduced by 1/√2 or 0.707 times.
