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Chapter 1: Problem 8

The Phoenix with a mass of \(350 \mathrm{~kg}\) was a spacecraft used for exploration of Mars. Determine the weight of the Phoenix, in \(\mathrm{N}\), (a) on the surface of Mars where the acceleration of gravity is \(3.73 \mathrm{~m} / \mathrm{s}^{2}\) and (b) on Earth where the acceleration of gravity is \(9.81 \mathrm{~m} / \mathrm{s}^{2}\).

Short Answer

Expert verified
The weight of the Phoenix on Mars is 1305.5 N, and on Earth, it is 3433.5 N.

Step by step solution

01

Understand the Formula for Weight

The weight of an object is given by the formula \( F = m \cdot g \) where \( F \) is the weight, \( m \) is the mass of the object, and \( g \) is the acceleration due to gravity.
02

Calculate Weight on Mars

Using the mass \( m = 350 \mathrm{~kg} \) and the acceleration due to gravity on Mars \( g = 3.73 \mathrm{~m}/\mathrm{s}^2 \), substitute these values into the formula: \[ F_{\text{Mars}} = 350 \mathrm{~kg} \times 3.73 \mathrm{~m}/\mathrm{s}^2 = 1305.5 \mathrm{~N} \]
03

Calculate Weight on Earth

Using the mass \( m = 350 \mathrm{~kg} \) and the acceleration due to gravity on Earth \( g = 9.81 \mathrm{~m}/\mathrm{s}^2 \), substitute these values into the formula: \[ F_{\text{Earth}} = 350 \mathrm{~kg} \times 9.81 \mathrm{~m}/\mathrm{s}^2 = 3433.5 \mathrm{~N} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

gravity
Gravity is a force that attracts two bodies toward each other. On Earth, it gives weight to physical objects and causes them to fall to the ground when dropped. The acceleration due to gravity is different on other planets. For instance, Mars has a lower gravitational force compared to Earth. The gravitational force on Earth is about 9.81 m/s2, while on Mars, it's approximately 3.73 m/s2. This means a spacecraft will weigh less on Mars than on Earth because the pull of gravity is weaker there. Hence, gravity not only affects an object's weight but also determines the force we experience daily.
mass
Mass is a measure of the amount of matter in an object. It is usually measured in kilograms (kg). Unlike weight, which varies based on location and the gravitational pull, mass remains constant regardless of where the object is. In the given exercise, the Phoenix spacecraft has a mass of 350 kg. This value does not change whether the spacecraft is on Mars, Earth, or in space. It is crucial to understand that mass is intrinsic to the object and differs from weight, which is the force exerted by gravity on that object.
Newton's second law
Newton's second law of motion states that the force acting on an object is equal to the mass of that object multiplied by its acceleration \[ F = m * a \]. This formula helps us understand how much force is needed to move an object with a certain mass. In the context of the exercise, this law is used to calculate the weight of the spacecraft on both Mars and Earth. Weight is a special case of force, where the acceleration is due to gravity. Therefore, the weight (force due to gravity) on Mars is calculated using its gravitational acceleration (3.73 m/s2), and on Earth using 9.81 m/s2. In simple terms, Newton's second law helps us convert mass into weight by considering the gravitational pull of the planet where the object is located.

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Most popular questions from this chapter

Air is contained in a vertical piston-cylinder assembly such that the piston is in static equilibrium. The atmosphere exerts a pressure of \(101 \mathrm{kPa}\) on top of the \(0.5\)-m-diameter piston. The gage pressure of the air inside the cylinder is \(1.2 \mathrm{kPa}\). The local acceleration of gravity is \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\). Subsequently, a weight is placed on top of the piston causing the piston to fall until reaching a new static equilibrium position. At this position, the gage pressure of the air inside the cylinder is \(2.8 \mathrm{kPa}\). Determine (a) the mass of the piston, in \(\mathrm{kg}\), and (d) the mass of the added weight, in \(\mathrm{kg}\).

Show that a standard atmospheric pressure of \(760 \mathrm{mmHg}\) is equivalent to \(101.3 \mathrm{kPa}\). The density of mercury is 13,590 \(\mathrm{kg} / \mathrm{m}^{3}\) and \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\).

Perform the following unit conversions: (a) \(1 \mathrm{~L}\) to in. \({ }^{3}\) (b) \(650 \mathrm{~J}\) to Btu (c) \(0.135 \mathrm{~kW}\) to \(\mathrm{ft} \cdot \mathrm{lbf} / \mathrm{s}\) (d) \(378 \mathrm{~g} / \mathrm{s}\) to \(\mathrm{lb} / \mathrm{min}\) (e) \(304 \mathrm{kPa}\) to \(\mathrm{lbf} / \mathrm{in}^{2}\) (f) \(55 \mathrm{~m}^{3} / \mathrm{h}\) to \(\mathrm{ft}^{3} / \mathrm{s}\) (g) \(50 \mathrm{~km} / \mathrm{h}\) to \(\mathrm{ft} / \mathrm{s}\) (h) \(8896 \mathrm{~N}\) to ton (=2000 lbf)

A gas contained within a piston-cylinder assembly undergoes four processes in series: Process 1-2: Constant-pressure expansion at 1 bar from \(V_{1}=0.5 \mathrm{~m}^{3}\) to \(V_{2}=2 \mathrm{~m}^{3}\) Process 2-3: Constant volume to 2 bar Process 3-4: Constant-pressure compression to \(1 \mathrm{~m}^{3}\) Process 4-1: Compression with \(p V^{-1}=\) constant Sketch the processes in series on a \(p-V\) diagram labeled with pressure and volume values at each numbered state.

A closed system consists of \(0.5 \mathrm{kmol}\) of ammonia occupying a volume of \(6 \mathrm{~m}^{3}\). Determine (a) the weight of the system, in \(\mathrm{N}\), and (b) the specific volume, in \(\mathrm{m}^{3} / \mathrm{kmol}\) and \(\mathrm{m}^{3} / \mathrm{kg}\). Let \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\).
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