/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 87 The energy, \(E\), needed to mov... [FREE SOLUTION] | 91Ó°ÊÓ

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The energy, \(E\), needed to move an object a distance \(d\) by applying a force \(F\) is \(E=F \times d\). What must be the SI unit of force if this equation is to be consistent with the SI unit of energy for \(E ?\)

Short Answer

Expert verified
The SI unit of force must be the Newton (N).

Step by step solution

01

Understand the given formula

The formula provided is \( E = F \times d \), where \( E \) is energy, \( F \) is force, and \( d \) is distance. Energy \( E \) is expressed in Joules (J) in the SI system, and distance \( d \) is measured in meters (m). We need to find the SI unit of force \( F \) so that the units balance in the equation.
02

Express the relationship with units

The equation \( E = F \times d \) can be expressed in terms of units as: \( \text{unit of } E = \text{unit of } F \times \text{unit of } d \). Since the unit of energy \( E \) is Joules (J) and the unit of distance \( d \) is meters (m), we have \( \text{J} = \text{unit of } F \times \text{m} \).
03

Solve for the unit of force

From the equation in Step 2: \( \text{J} = \text{unit of } F \times \text{m} \), we can rearrange to solve for the unit of force: \( \text{unit of } F = \frac{\text{J}}{\text{m}} \). Since the Joule (J) is defined as \( \text{kg} \cdot \text{m}^2/\text{s}^2 \), substituting this back, we get \( \text{unit of } F = \frac{\text{kg} \cdot \text{m}^2/\text{s}^2}{\text{m}} = \text{kg} \cdot \text{m/s}^2 \).
04

Recognize the derived unit

The unit \( \text{kg} \cdot \text{m/s}^2 \) is defined as a Newton (N) in the SI system. Therefore, the SI unit of force \( F \) that makes the equation consistent is the Newton.

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Key Concepts

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

Energy in Physics
Energy is a fundamental concept in physics. It describes the ability to perform work or produce change. Energy exists in various forms, such as kinetic, potential, thermal, and chemical energy.
In physics, the standard unit for energy is the Joule (J). A Joule represents the energy transferred when a force of one Newton moves an object one meter. This description ties directly into the problem at hand – calculating energy using force and distance in the formula \( E = F \times d \).
The law of conservation of energy is central in physics. It states that energy cannot be created or destroyed, only transformed. This principle allows energy to be a crucial tool in solving physical problems, like finding the necessary force to move an object a given distance.
Force Calculation
Calculating force involves understanding both the magnitude and direction of interaction between two or more objects. In physics, force is a vector quantity, meaning it has both size and direction.
The fundamental formula for force is expressed as \( F = ma \), where \( m \) is mass and \( a \) is acceleration. Hence, the unit of force in the SI system is Newton (N), defined as \( \text{kg} \cdot \text{m/s}^2 \). This directly results from applying Newton’s second law of motion.
When working with equations involving force, such as \( E = F \times d \), you ensure units consistency. Multiplying a force by a distance gives you energy, which is measured in Joules. The units beautifully connect with the problem, helping verify the calculation.
Newton's Laws
Newton's Laws of Motion are the foundation of classical mechanics. These laws describe the relationship between an object and the forces acting on it.
1. **First Law**: Sometimes called the law of inertia, it states that an object at rest remains at rest, and an object in motion continues in motion with the same speed and in the same direction unless acted upon by a nonzero net force.
2. **Second Law**: Provides a quantitative description of the changes that a force can produce on the motion of a body. It is represented by the equation \( F = ma \), signifying that force is the product of mass and acceleration. This equation defines the unit of force, the Newton, which is used in the original exercise.
3. **Third Law**: States that for every action, there is an equal and opposite reaction. This means that forces always come in pairs, acting on interacting objects.
These laws are not only integral to understanding mechanics but also critical in areas such as energy computations, illustrating how forces dictate the energy transfer during motion or interaction.

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