Ford v Ferrari

Day 1: Speed, Turning, and Braking

Problem 1

In Ford v Ferrari, race cars must accelerate rapidly out of corners. Suppose a car increases its speed from \(v_i = 32\ {\rm m/s}\) to \(v_f = 48\ {\rm m/s}\) in \(\Delta t = 5.0\ {\rm s}\). Assume the acceleration is constant.

(a) What is the average acceleration?

(b) If the car mass is \(m = 1.1\times 10^3\ {\rm kg}\), what average net force acts on the car?

(c) How far does the car travel during this interval?

Problem 2

A race car turns through a curve at high speed. Suppose the car enters a flat turn of radius \(r = 140\ {\rm m}\) at speed \(v = 44\ {\rm m/s}\).

(a) What centripetal acceleration is required?

(b) What centripetal force is required for a \(1.1\times 10^3\ {\rm kg}\) car?

(c) What minimum coefficient of static friction is needed to negotiate the turn without skidding?

Problem 3

Braking performance is critical during endurance racing. Suppose a car slows uniformly from \(v_i = 68\ {\rm m/s}\) to \(v_f = 28\ {\rm m/s}\) over a distance of \(d = 260\ {\rm m}\).

(a) What is the car’s acceleration?

(b) How long does the braking take?

(c) If the car mass is \(1.1\times 10^3\ {\rm kg}\), what average braking force acts on the car?

Day 2: Power and Energy

Problem 4

At high speed, aerodynamic drag becomes important. Assume a car has drag coefficient \(C_D = 0.42\), frontal area \(A = 1.8\ {\rm m^2}\), air density \(\rho = 1.20\ {\rm kg/m^3}\), and speed \(v = 62\ {\rm m/s}\). Use \(F_D = \frac{1}{2}C_D \rho A v^2.\)

(a) What drag force acts on the car?

(b) What power is required just to overcome this drag at that speed?

Problem 5

A race car’s kinetic energy changes dramatically during acceleration. Suppose a \(1.1\times 10^3\ {\rm kg}\) car speeds up from \(v_i = 30\ {\rm m/s}\) to \(v_f = 65\ {\rm m/s}\). Neglect drag and rolling losses for part (d).

(a) What is the initial kinetic energy?

(b) What is the final kinetic energy?

(c) What is the change in kinetic energy?

(d) If this change occurs in \(8.0\ {\rm s}\), what is the average power associated with the change in kinetic energy?

Problem 6

During a pit stop, reducing the time the car is stationary is critical. Suppose a car enters the pit lane at \(v_i = 24\ {\rm m/s}\) and brakes uniformly to rest over \(d = 68\ {\rm m}\). Assume straight-line motion.

(a) What acceleration is required?

(b) How long does the car take to stop?

(c) If the driver later accelerates from rest back to \(24\ {\rm m/s}\) in \(6.0\ {\rm s}\), what average acceleration is required?