Question

You are riding your bicycle down the street at a speed of 14 m/s. Your bicycle frame has a mass of 6.6 kg, and each of its two wheels has mass 2.2 kg and radius 0.35 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules), taking into account both the translational and rotational motion

Answer 1

1078 Joules

Step-by-step explanation:

The computation of the total kinetic energy of the bicycle is shown below:

Given that

mass of bicycle's frame (m) = 6.6 kg

mass of each wheel (M) = 2.2 kg

radius of each wheel (r) = 0.35 m

And, the linear speed (v) = 14 ms

Now

As we know that

Angular velocity (ω) = v ÷ r

= 140 ÷ .35

= 40 rads

Total kinetic energy = translational kinetic energy + rotational kinetic energy

= (1 ÷2 × m × v^2) + (2 × 1 ÷ 2×I × ω^2)

= (0.5 × 6.6 × [14]^2) + (M × r2 × ω^2)

= 646.8 + (2.2 × 0.35 × 0.35 × [40]^2)

= 646.8 + 431.2

= 1078 Joules