Question

a child is riding a bike at a speed of 0.6m/s with a total kinetic energy of 12.4J.If the mass of the child is 30kg, what is the mass of the bike?

Answer 1

Ek=kinetic energy  (J)
m=mass of object (Kg)
v=speed of object  (m/s)

We have the following formula:

Ek=(1/2)mv²   ⇒ m=2(Ek)/v²

In this case:
m= mass of the child + mass of the bike
m=30 kg + m₁       (m₁=mass of the bike).

We would have to modify our formula like this:

m=2(Ek)/v²
m=30 kg + m₁


30 kg +m₁=2(Ek)/v²
m₁=2(Ek)/v²-30 kg

We have the following data:

v=0.6 m/s
Ek=12.4J
m=30 Kg + m₁

Therefore:

m₁=2(Ek)/v²  - 30 kg
m₁=2(12.4 J)/(0.6 m/s)²  - 30 kg
m₁=24.8 J/(0.36 m²/s²)  -30 kg
m₁=68.89 Kg - 30 kg
m₁=38.89 Kg

Answer: the mass of the bike is 38.89 Kg. 

Answer 2

The mass of the bike is 38.89 Kg.