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Chapter 4: Problem 12

(a) What is the mass of a book that weighs 3.20 \(\mathrm{N}\) in the laboratory? (b) In the same lab, what is the weight of a dog whose mass is 14.0 \(\mathrm{kg} ?\)

Short Answer

Expert verified
(a) 0.326 kg (b) 137.34 N

Step by step solution

01

Understanding Weight and Mass

Weight is the force with which an object is pulled towards the Earth and is given by the equation \( W = m \times g \), where \( W \) is the weight, \( m \) is the mass, and \( g \) is the acceleration due to gravity. On Earth, \( g \) is approximately \( 9.81 \, \mathrm{m/s^2} \).
02

Calculation of Mass from Weight

To find the mass of the book, rearrange the formula for weight: \( m = \frac{W}{g} \). Substitute the given values, \( W = 3.20 \, \mathrm{N} \) and \( g = 9.81 \, \mathrm{m/s^2} \), to find \( m \).\[m = \frac{3.20}{9.81} \approx 0.326 \, \mathrm{kg}\]
03

Calculation of Weight from Mass

To find the weight of the dog, use the same weight formula. You are given \( m = 14.0 \, \mathrm{kg} \) and \( g = 9.81 \, \mathrm{m/s^2} \). Calculate the weight \( W \).\[W = 14.0 \times 9.81 = 137.34 \, \mathrm{N}\]

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Key Concepts

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

Force and Weight
In the realm of physics, understanding the concept of force and weight is crucial. Weight is a type of force that acts on every object with mass. Specifically, it's the gravitational force exerted on an object due to Earth's gravitational pull.

When we speak of weight, we use the formula:
  • \( W = m \times g \)
where \( W \) represents the weight, \( m \) is the mass of the object, and \( g \) is the acceleration due to gravity, which on Earth is approximately \( 9.81 \, \mathrm{m/s^2} \).

This formula shows that weight is directly proportional to both mass and gravity, meaning a greater mass or a larger gravitational pull results in a greater weight. In physics problems, determining either mass from weight or vice-versa involves rearranging this basic equation.
Mass and Gravity
Mass is a fundamental property of an object, representing the amount of matter it contains, and unlike weight, mass does not change regardless of location. Mass is often measured in kilograms in the metric system.

Gravity, on the other hand, is a natural force that draws objects towards each other. On Earth, this force is quantified by the acceleration due to gravity, denoted by \( g \).

Understanding how mass and gravity relate is essential for exploring how objects behave under gravitational forces. For instance, if you know the weight of an object and want to find its mass, you rearrange the weight formula:
  • \( m = \frac{W}{g} \)
This allows you to find mass by dividing the weight by the gravitational acceleration, making it helpful in practical problems, just like the given exercise of determining the mass of a book given its weight.
Physics Calculations
Physics involves calculations that utilize established formulas to solve real-world problems. These calculations help you move between concepts like force, weight, mass, and gravity effectively.

For example, if you know an object's mass and wish to find its weight, you multiply the mass by the gravitational acceleration:
  • \( W = m \times g \)
In the exercise provided, such calculation allows us to find out the weight of a dog by applying this formula.

Conversely, if given weight, you can determine mass through the formula:
  • \( m = \frac{W}{g} \)
These processes exemplify core physics calculations that take place regularly in problem-solving scenarios.

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Most popular questions from this chapter

A 275 \(\mathrm{N}\) bucket is lifted with an acceleration of 2.50 \(\mathrm{m} / \mathrm{s}^{2}\) by a 125 \(\mathrm{N}\) uniform vertical chain. Start each of the following parts with a free-body diagram. Find the tension in (a) the top link of the chain, (b) the bottom link of the chain, and (c) the middle link of the chain.

A parachutist relies on air resistance (mainly on her parachute) to decrease her downward velocity. She and her parachute have a mass of 55.0 \(\mathrm{kg}\) , and at a particular moment air resistance exerts a total upward force of 620 \(\mathrm{N}\) on her and her parachute. (a) What is the weight of the parachutist? \((\mathrm{b})\) Draw a free-body diagram for the parachutist (see Section \(4.6 ) .\) Use that diagram to calculate the net force on the parachutist. Is the net force upward or downward? (c) What is the acceleration (magnitude and direction) of the parachutist?

You drag a heavy box along a rough horizontal floor by a horizontal rope. Identify the reaction force to each of the following forces: (a) the pull of the rope on the box, (b) the friction force on the box, (c) the normal force on the box, and (d) the weight of the box.

A tennis ball traveling horizontally at 22 \(\mathrm{m} / \mathrm{s}\) suddenly hits a vertical brick wall and bounces back with a horizontal velocity of 18 \(\mathrm{m} / \mathrm{s}\) . Make a free-body diagram of this ball (a) just before it hits the wall, (b) just after it has bounced free of the wall, and (c) while it is in contact with the wall.

The space shuttle. During the first stage of its launch, a space shuttle goes from rest to 4973 \(\mathrm{km} / \mathrm{h}\) while rising a vertical distance of 45 \(\mathrm{km}\) . Assume constant acceleration and no variation in \(g\) over this distance. (a) What is the acceleration of the shuttle? (b) If a 55.0 \(\mathrm{kg}\) astronaut is standing on a scale inside the shuttle during this launch, how hard will the scale push on her? Start with a free-body diagram of the astronaut. (c) If this astronaut did not realize that the shuttle had left the launch pad, what would she think were her weight and mass?
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