Answer:
a) Ktotal = 71.85 J
b) Ktotal = 71.85 J
Explanation:
a) The total kinetic energy is that of the total mass of the bicycle plus the rotational kinetic energy of the two wheels. The linear speed of the circumference of the wheels matches the forward speed of the bicycle, so their angular speed is
ω = v/r
The moment of inertia of one solid disk bicycle wheel is
I = 0.5*m₂*r²
And the rotational kinetic energy of one wheel is
Kr = 0.5*I*ω² = 0.5*(0.5*m₂*r²)*(v/r)² = 0.25*m₂*v²
The total kinetic energy is then that of the frame and wheels plus the rotational kinetic energy.
Ktotal = 0.5*(m₁ + 2*m₂)*v² + 2*(0.25*m₂*v²)
⇒ Ktotal = 0.5*v²*(m₁ + 3*m₂)
where
m₁ = 6.75 Kg
m₂ = 0.820 kg
v = 3.95 m/s
then
⇒ Ktotal = 0.5*(3.95 m/s)²*(6.75 Kg + 3*0.820 kg)
⇒ Ktotal = 71.85 J
b) We can apply the same equation obtained before
⇒ Ktotal = 0.5*v²*(m₁ + 3*m₂)
where
m₁ = 675 Kg
m₂ = 82.0 kg
v = 0.395 m/s
then
⇒ Ktotal = 0.5*(0.395 m/s)²*(675 Kg + 3*82 kg)
⇒ Ktotal = 71.85 J
