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Chapter 2: Problem 18

The doozy is defined as the unit of force required to accelerate a unit of mass, called the cuz, with the gravitational acceleration on the surface of the moon, which is one-sixth of the normal gravitational acceleration on earth. (a) What is the conversion factor that would be used to convert a force from the natural unit to the derived unit in this system? (Give both its numerical value and its units.) (b) What is the weight in doozies of a 3 -cuz object on the moon? What does the same object weigh in Lizard Lick, North Carolina?

Short Answer

Expert verified
The conversion factor is \(1.62 N/doozy\). A 3-cuz object would weigh 3 doozies or \(4.86 N\) on the moon, and 18.17 doozies or \(29.43 N\) in Lizard Lick, North Carolina.

Step by step solution

01

Understand the definition of doozy

Our new unit of force, the doozy, is said to be the force required to accelerate one 'cuz' with the gravity of the moon. This means 1 doozy = 1 cuz * moon gravitational acceleration. The latter is commonly given as \(1.62 m/s^2\). So 1 doozy equals the force to accelerate 1 cuz by \(1.62 m/s^2\)
02

Find the conversion factor to newtons

We can think of a force of 1 doozy as a force of 1 cuz * \(1.62 m/s^2\). To convert this to newtons, we can think of the 'cuz' as a unit of mass and set it equal to one kilogram. This gives us the conversion factor 1 doozy = \(1.62 N\).
03

Calculate the 3-cuz object's weight on the moon

Weight is defined as mass times gravitational acceleration. Therefore, the weight of the object on the moon in doozies is 3 cuz * 1 = 3 doozies. To convert this to newtons, we use our conversion factor 1 doozy = \(1.62 N\), which gives us a weight on the moon of \(3 * 1.62 N = 4.86 N\).
04

Calculate the object's weight in Lizard Lick, North Carolina

On earth, the gravitational acceleration is \(9.81 m/s^2\). Therefore, the weight of the object in Lizard Lick in newtons is 3 kg * \(9.81 m/s^2\) = \(29.43 N\). To convert this to doozies, we divide by our conversion factor to find that the weight in North Carolina equals \(29.43 N / 1.62(doosies/N) = 18.17 doozies\).

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Key Concepts

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

Gravitational Acceleration
Gravitational acceleration is a fundamental concept in physics. It describes the rate at which an object accelerates due to gravity alone. This acceleration depends on the celestial body you are on. For example, Earth's gravitational acceleration is a constant value of approximately \(9.81 \, m/s^2\). This means that any object in freefall near the Earth's surface will accelerate downwards at this rate.

However, when you are on the moon, gravitational acceleration reduces significantly. It is only about \(1.62 \, m/s^2\). This is roughly one-sixth the strength of Earth's gravity. This difference drastically affects how objects move and how much they "weigh" in terms of gravitational force. In physics problems, knowing the gravitational acceleration on different celestial bodies helps in calculating factors like weight and force.
  • Gravitational acceleration determines how much an object will fall or weigh.
  • On the moon, you experience one-sixth of Earth's gravitational pull.
  • This change is essential in calculations for physics exercises.
Force Measurement
Force is measured based on how much it can accelerate an object. The SI unit of force is the newton (N), defined as the force needed to accelerate one kilogram of mass by one meter per second squared. However, in certain contexts, alternative units are used鈥攍ike the fictional 'doozy' in this exercise.

The doozy is the force unit required to accelerate an object with mass in "cuz" at the moon's gravitational pull. Recognizing that force depends on both mass and acceleration is crucial for understanding unit conversion. For example, 1 doozy can be translated into classical units as \(1.62\, N\), since on the moon, the gravitational acceleration is \(1.62 \, m/s^2\).
  • Force involves both mass and acceleration.
  • The conversion between force units helps in solving problems.
  • Knowing alternative units like doozy expands physics problem-solving strategies.
Weight Calculation
Weight is essentially a measure of the force exerted on an object due to gravitational pull. To calculate weight, we multiply the object's mass by the gravitational acceleration of the location we are considering. Hence, the formula for weight is:\[\text{Weight} = \text{mass} \times \text{gravitational acceleration}\]
On the moon, an object's weight is much lesser than on Earth due to the reduced gravity. In our example, a 3-cuz mass weighs 3 doozies on the moon. In conversion terms, 3 doozies equals about \(4.86 \, N\) on the moon because \(1 \, \text{doozy} = 1.62 \, N\). When the same object is considered on Earth, the weight is greater, calculated at \(29.43 \, N\), and accordingly \(18.17\) doozies. Understanding this conversion is important for interplanetary comparisons.
  • Weight changes with gravitational acceleration.
  • On the moon, objects weigh less than on Earth.
  • Conversion between weight units helps understand these differences.

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