Chapter 6: Problem 1
If the force exerted by the intern is doubled and the distance is halved, does the work done by the intern increase, decrease, or remain the same?
Short Answer
Expert verified
The work done remains the same.
Step by step solution
01
Understanding the Formula for Work
Work can be calculated using the formula \( W = F \times d \), where \( W \) is the work done, \( F \) is the force applied, and \( d \) is the distance over which the force is applied.
02
Initial Conditions
Initially, let the force be \( F \) and the distance be \( d \). Therefore, the initial work \( W_0 = F \times d \).
03
New Conditions
The force is doubled, so the new force is \( 2F \). The distance is halved, so the new distance is \( \frac{d}{2} \).
04
Calculate the New Work Done
Using the new conditions, the work done is \( W_1 = (2F) \times \left( \frac{d}{2} \right) = 2F \times \frac{d}{2} = F \times d \).
05
Compare the Initial and New Work
Comparing \( W_0 = F \times d \) and \( W_1 = F \times d \), we see that \( W_1 = W_0 \). This means the work done remains the same.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Force
Force is a fundamental concept in physics that describes a push or pull on an object. This interaction causes changes in the motion of the object, whether it translates, accelerates, or maintains its state. The unit of force in the International System of Units (SI) is the Newton (N).
- Force is vector-based, meaning it has both magnitude and direction. For example, pushing a door open involves force with a specific magnitude and direction.
- In the context of work and energy, force plays a significant role since itβs a key factor in doing work on an object.
- The formula for force is given by Newton's second law: \( F = m imes a \), where \( F \) represents force, \( m \) is mass, and \( a \) is acceleration.
Distance
Distance refers to the amount of space between two points. In physics, it determines how far an object travels, which is essential when calculating work. Unlike displacement, which considers direction, distance is a scalar quantity, meaning only magnitude is taken into account.
- Distance comes into play in the formula for workβit is the path over which the force acts.
- The SI unit for distance is the meter (m).
- If the distance over which a force is applied changes, it directly affects the work done. For instance, in our problem set, halving the distance while doubling force maintained the same amount of work.
Formula for Work
The formula for work is a simple yet powerful tool in understanding how force affects motion over a specific distance. Work is computed by the equation \( W = F \times d \), where \( W \) represents work, \( F \) is force, and \( d \) is distance.
- Work is measured in Joules (J), with one Joule equivalent to one Newton-meter.
- If the force applied or the distance changes, the amount of work done can increase, decrease, or remain the same; it depends on how these two factors interact.
- In scenarios like the one presented in the original exercise, understanding work helps explain energy transfer in situations where force and distance vary.
- Through doubling force and halving distance, the interplay of these variables showed that work remained unchangedβcounterintuitive but true when applied correctly.