Question

Jack rides his bicycle along a level road and has a total kinetic energy od 1440J. He brakes, exerting a force of 200N on the wheels. a) How far does he travel before he stops? b) What happens to temputure of the brakes? Explai your answer.

Answer 1

(a) 7.2 m
(b) The temperature of the brakes will rise.

Explanation:

(a) Use the braking force and initial kinetic energy to work out the distance required to brake to zero kinetic energy.
`W = E_k = Fd ⇒ d = E_k/F`
`⇒ d = 1440 / 200 = 7.2 m`

(b) Brakes convert kinetic energy into heat. The heat will increase the temperature of the brakes. The amount of temperature rise will depend on the heat capacity of the material that the brakes are made of. The temperature rise is given by:
`Δθ = (ΔQ)/(mc)`
Where ΔQ is the heat energy added to the brakes¹,
m is the mass of the brakes,
c is the specific heat capacity of the material the brakes are made of.

¹ The heat energy added to the brakes will be approximately equal to the kinetic energy lost by the bicycle.

===

Example calculations
Assumption equal amounts of heat will be transferred to the rim of the wheel and to the brake pads. So half of the total heat energy (1440 J) will be transferred to the pads and the other half will be transferred to the rim of the wheel.
Data:
Specific heat capacity of brake pad: `c_p` = 900 J kg⁻¹ K⁻¹
Specific heat capacity of wheel rim: `c_r` = 460 J kg⁻¹ K⁻¹
Mass of brake pads: `m_p` = 0.100 kg
Mass of wheel rim: `m_r` = 0..550 kg

Temperature rise for pads:
`Δθ_p = (ΔQ_p)/(m_p × c_p) = 720 / (0.100 × 900) = 8.0 ºC`

Temperature rise for rims:
`Δθ_r = (ΔQ_r)/(m_r × c_r) = 720 / (0.550 × 460) = 2.8 ºC`