Work, Power, and Simple Machines Study Guide

Principles of Work and Power

• Definition of Work: In the field of science, work is defined as the transfer of energy to an object by a force that causes that object to move in the same direction as the force.
• Condition for Work: Work is strictly considered to be done only while the force is being actively applied to the object.
• Formula for Work:
  • $\text{Work (in Joules / } J) = \text{Force (in Newtons / } N) \times \text{Distance (in meters / } m)$
  • $W = F \times d$
• Application Example: If a person pushes a book for a distance of $0.25\,m$ and the book continues to slide for another $1\,m$ after the person stops pushing, the distance used to calculate the work performed by the person is only the $0.25\,m$ during which the force was applied.

Calculating Work, Force, and Distance

Work Calculation Problems

• Problem 1 (Maria and the Box): Maria pushes a box with a force of $20\,N$ across the floor for a distance of $3\,m$.
  • $\text{Solution: } 20\,N \times 3\,m = 60\,J$
• Problem 2 (Cart Pulling): A boy pulls a cart using $15\,N$ of force for $4\,m$.
  • $\text{Solution: } 15\,N \times 4\,m = 60\,J$
• Problem 3 (Stair Climb): A student weighing $400\,N$ climbs up a staircase that is $3\,m$ high.
  • $\text{Work against gravity: } 400\,N \times 3\,m = 1200\,J$
• Work Comparison:
  • Case A: $10\,N$ force over $5\,m = 50\,J$
  • Case B: $20\,N$ force over $2\,m = 40\,J$
  • Conclusion: Case A involves more work ($50\,J > 40\,J$).

Force Calculation Problems

• Formula: $F = \frac{W}{d}$
• Problem 1: A worker does $120\,J$ of work moving a box $4\,m$.
  • $\text{Force: } \frac{120\,J}{4\,m} = 30\,N$
• Problem 2: A person lifts a load through $2\,m$ while doing $100\,J$ of work.
  • $\text{Force: } \frac{100\,J}{2\,m} = 50\,N$
• Problem 3: A student does $250\,J$ of work to push a box $5\,m$.
  • $\text{Force: } \frac{250\,J}{5\,m} = 50\,N$
• Problem 4: It takes $450\,J$ of work to move a suitcase $3\,m$.
  • $\text{Force: } \frac{450\,J}{3\,m} = 150\,N$

Distance Calculation Problems

• Formula: $d = \frac{W}{F}$
• Problem 1: A force of $25\,N$ performs $200\,J$ of work.
  • $\text{Distance: } \frac{200\,J}{25\,N} = 8\,m$
• Problem 2: An applied force of $50\,N$ produces $400\,J$ of work.
  • $\text{Distance: } \frac{400\,J}{50\,N} = 8\,m$
• Problem 3: A student exerts a force of $10\,N$ and does $70\,J$ of work.
  • $\text{Distance: } \frac{70\,J}{10\,N} = 7\,m$
• Problem 4: A force of $60\,N$ does $180\,J$ of work.
  • $\text{Distance: } \frac{180\,J}{60\,N} = 3\,m$

Understanding Power

• Definition of Power: Power represents the rate at which work is performed. It describes how fast work is being done.
• Formula for Power:
  • $\text{Power (in Watts / } W) = \frac{\text{Work (in Joules / } J)}{\text{Time (in seconds / } s)}$
  • $P = \frac{W}{t}$
  • Since $W = F \times d$, the formula can also be written as $P = \frac{F \times d}{t}$.
• Relationship to Speed: The faster work is accomplished, the higher the power output. For example, running up stairs generates more power than walking up the same stairs slowly.

Common Power Scenarios and Problems

• A car problem: A car exerts a force of $500\,N$ to move $100\,m$ in $50\,s$.
  • $\text{Work: } 500\,N \times 100\,m = 50,000\,J$
  • $\text{Power: } \frac{50,000\,J}{50\,s} = 1000\,W$
• Crate movement: A $100\,N$ force moves a crate $12\,m$ in $6\,s$.
  • $\text{Work: } 100\,N \times 12\,m = 1200\,J$
  • $\text{Power: } \frac{1200\,J}{6\,s} = 200\,W$
• Object movement: A $50\,kg$ object moves $20\,m$ in $5\,s$. Note: Standard gravity ($9.8\,m/s^2$ or approximately $10\,m/s^2$) would be needed to find weight/force if it is being lifted, but often mass problems in these slides use the force value provided.
• Motor lifting: A motor generates $500\,W$ while lifting a $200\,N$ load for $4\,s$.
  • $\text{Work: } \text{Power} \times \text{Time} = 500\,W \times 4\,s = 2000\,J$
• Staircase Force: A $75\,kg$ person climbs a staircase $5\,m$ high in $10\,s$.
  • $\text{Force (Weight): } 75\,kg \times 9.8\,m/s^2 = 735\,N \text{ (approximate)}$
• Time calculation: Work is $3000\,J$ with a power of $500\,W$.
  • $\text{Time: } \frac{W}{P} = \frac{3000\,J}{500\,W} = 6\,s$

Factors Affecting Work and Lifting

• Force at an Angle: When force is applied at an angle, it is composed of a downward force and a forward force. Only the component of the force in the direction of motion contributes to the work done.
• Work while Lifting Objects: When lifting an object vertically, the work done is equal to the weight of the object (force of gravity) multiplied by the vertical distance it is lifted.
• Relationship to Energy: Lifting an object increases the object's potential energy. The work done on the object is effectively stored as energy.

Simple Machines

Simple machines are devices that perform work using only a single motion. There are six primary types:

1. The Lever

• Definition: A bar that pivots or rotates around a fixed point called a fulcrum.
• First-Class Lever:
  • The fulcrum is positioned between the input force and the output force.
  • The direction of the input force is always different from the output force.
  • Examples: Seesaw, scissors, pliers, a hammer pulling a nail, a beverage can finger tab.
• Second-Class Lever:
  • The output force is positioned between the input force and the fulcrum.
  • Both forces act in the same direction.
  • This lever increases the output force relative to the input force.
  • Examples: Wheelbarrow, nutcracker, the human foot, stapler.
• Third-Class Lever:
  • The input force is between the output force and the fulcrum.
  • The output force is less than the input force.
  • Both forces act in the same direction.
  • Examples: Tweezers, rake, broom.

2. Wheel and Axle

• Definition: An axle (a shaft) attached to the center of a larger wheel so that they rotate together.
• Mechanics: The handle (larger diameter) acts as the wheel, and the shaft acts as the axle.
• Examples: Screwdriver, bicycle, doorknob, vehicle wheels, Ferris wheel, water faucet handle.

3. Inclined Plane

• Definition: A flat, sloped surface (a ramp).
• Examples: Skateboard ramp, slide, funnel, roof, water slide, road ramp.

4. Wedge

• Definition: A type of inclined plane with one or two sloping sides that moves.
• Example: A tooth.

5. Screw

• Definition: An inclined plane that is wrapped around a cylinder.
• Example: Threads of a lightbulb.

6. Pulley

• Definition: A grooved wheel with a rope or cable wrapped around it.
• Types:
  • Fixed Pulley: Changes the direction of the force.
  • Movable Pulley: Decreases the input force required to lift a load.
  • Pulley System: A combination of fixed and movable pulleys.
  • Example: Flagpole.

Compound Machines

• Definition: A machine formed when two or more simple machines work together in conjunction.
• Example: Can Opener
  • Uses a second-class lever to move the handle.
  • Uses a wheel and axle to turn the cutting blade.
  • Uses a wedge to puncture the lid of the metal can.

Class Activities and Exercises

Matching Simple Machines

• Tooth $\rightarrow$ Wedge
• Doorknob $\rightarrow$ Wheel and Axle
• Threads of a lightbulb $\rightarrow$ Screw
• Wheelbarrow $\rightarrow$ Lever
• Ramp $\rightarrow$ Inclined Plane
• Flagpole $\rightarrow$ Pulley

Group Relay Game

• 1. The first player solves a problem.
• 2. The answer is whispered to the next player in line.
• 3. The first player moves to the back, and the next player receives a new problem.
• 4. Group with the highest points for correct answers wins.

Poster Project Requirements

• Poster 1 - Work: Focus on the definition (force causing movement). Draw real-life examples like lifting a backpack, pushing a shopping cart, or pulling a wagon.
• Poster 2 - Power: Focus on the rate of work. Draw examples of high power, such as riding a bike fast, running up stairs, or using a lawnmower.
• Section Breakdown:
  • Section A: Key Ideas (definitions and formulas).
  • Section B: Sample Problems (2 original word problems with units: $N, m, J, s, W$).
  • Section C: Real-Life Examples (list at least 3, such as lifting bags or pushing chairs, and illustrate at least one).