The Right Stuff

The Right Stuff#

Day 1: Cars, Gold, and MotionFlight, Acceleration, and Forces#

Problem 1

In The Right Stuff, test pilots and astronauts experience very large accelerations during powered flight.

Suppose a pilot and seat together have a total mass of \(m = 95\ {\rm kg}\) and the pilot experiences an upward acceleration of \(a = 4.5g\) during launch, where \(g = 9.81\ {\rm m/s^2}\).

(a) What is the magnitude of the pilot’s acceleration in \({\rm m/s^2}\)?

(b) What net upward force is required to produce this acceleration?

(c) What is the upward force exerted by the seat on the pilot?

Assume the pilot is moving vertically upward.

Problem 2

During high-speed test flights, an aircraft must generate enough lift to support its weight. Suppose an aircraft has mass \(m = 7.2\times 10^3\ {\rm kg}\).

(a) What is the weight of the aircraft?

(b) If the aircraft is flying straight and level at constant speed, what lift force must the wings provide?

(c) If the aircraft begins pulling upward with an acceleration of \(a = 12\ {\rm m/s^2}\), what lift force is then required?

Problem 3

In one test-flight scenario, an aircraft moving at high speed must turn without losing control.

Suppose an aircraft travels at speed \(v = 210\ {\rm m/s}\) through a circular turn of radius \(r = 1.8\times 10^3\ {\rm m}\).

(a) What centripetal acceleration is required?

(b) If the aircraft mass is \(m = 7.2\times 10^3\ {\rm kg}\), what centripetal force is required?

(c) Express the centripetal acceleration as a multiple of \(g\).

Day 2: Gravitation, Orbit, and Reentry#

Problem 4

The early Mercury missions in The Right Stuff involve the transition from suborbital flight to true orbital flight. Assume a spacecraft is placed into a circular orbit at altitude \(h = 180\ {\rm km}\) above Earth.

Use the following values:

  • Mass of Earth: \(M_E = 5.97\times 10^{24}\ {\rm kg}\)

  • Radius of Earth: \(R_E = 6.37\times 10^6\ {\rm m}\)

  • Universal gravitation constant: \(G = 6.67\times 10^{-11}\ {\rm N\,m^2/kg^2}\)

(a) What is the orbital radius of the spacecraft?

(b) What orbital speed is required for a circular orbit at this altitude?

(c) Explain why reaching orbit requires much more than simply going to a high altitude.

Problem 5

A returning capsule must survive reentry through the atmosphere. We can estimate the scale of the kinetic energy involved. Suppose a capsule of mass \(m = 1.9\times 10^3\ {\rm kg}\) enters the atmosphere with speed \(v = 7.8\times 10^3\ {\rm m/s}\).

(a) What is the kinetic energy of the capsule?

(b) If \(3.0\%\) of this kinetic energy is transferred to the heat shield, how much thermal energy does the heat shield absorb?

(c) Based on this result, explain why reentry is such a severe thermal problem.

Problem 6

After reentry, the Mercury capsule descends under parachute before splashdown. Suppose the capsule mass is \(m = 1.9\times 10^3\ {\rm kg}\) and it descends vertically at a constant speed of \(v = 9.0\ {\rm m/s}\).

(a) What is the weight of the capsule?

(b) If the capsule is descending at constant speed, what must the upward drag force from the parachute be?

(c) If the capsule instead slows from \(9.0\ {\rm m/s}\) to \(3.0\ {\rm m/s}\) in \(2.5\ {\rm s}\) just before splashdown, what average upward net force acts on the capsule during that interval?

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