The disc brakes of a high performance car are often made of carbon fiber instead of iron,thereby reducing the mass.If both types of discs are of the same size and shape,and each iron disc has a mass of 4 kg and each carbon disc has a mass of 1 kg,what is the reduction in rotational kinetic energy at 72 km/h if all the four iron discs in the car are replaced with carbon discs?
A)300 J
B)400 J
C)800 J
D)1200 J
E)1600 J

Question

Quizplus · Accepted Answer

The reduction in mass for each disc is 3 kg (4 kg - 1 kg). For four discs, the total mass reduction is 12 kg. The reduction in rotational kinetic energy is calculated using the formula: ΔKE = 0.5 * ΔI * ω², where ΔI is the change in moment of inertia and ω is the angular velocity. Since the discs are the same size, ΔI = Δm * r². Assuming the car's wheels have a radius r, the reduction in rotational kinetic energy is 0.5 * 12 kg * (v/r)², where v = 72 km/h = 20 m/s. Simplifying, the reduction is 1200 J.

The Disc Brakes of a High Performance Car Are Often