Chapter 4Work and Energy Section 1: Work and Machines Section 2: Describing Energy Section 3: Conservation of Energy
Section 1: Work and Machines Work – the transfer of energy that occurs when a force makes an object move • no movement, no work • direction of the net force indicates where or on what work is being done • calculating work:equation for work: work = force x distance, or: Example: How much work is done if Reggie lifts a box, m = 50-kg, 1.75 meters? Solution:
Section 1: Work and Machines Machine – a device that makes doing work easier • Machines make doing work easier in three ways: • Increasing the force applied to the objectexample: a car jack to lift a car to change a flat tire • Increasing the distance over which the force is appliedexample: using a ramp to raise objects to a height • Changing the direction of the applied forceexample: a wedge – the vertical force is changed to a horizontal force • Work done by machines • Two forces are involved when a machine is used to do work: • Effort force – the force applied to the machine • Resistance force – the force applied by the machine to overcome resistance • Conservation of Energy • You transfer energy to a machine, the machine transfers that energy to the object • Energy is neither created nor destroyed, so the work done by the machine is never greater than the work done to the machine • Because of energy losses due to friction, the work done by the machine is always less than the work done to the machine
Section 1: Work and Machines • Mechanical Advantage – the number of times a machine multiplies the effort force • Equation for Mechanical Advantage : Example: A claw hammer is used to pull a nail from a board. If the claw exerts a resistance force of 2500-N to the applied force of 125-N, what is the mechanical advantage of the hammer?Solution: Notice that the force units (N) cancel; mechanical advantage has no units, it is just a number.
Section 1: Work and Machines Simple machine – a machine that does work with only one movement • There are six (6) simple machines divided into two types: Compound machine – a machine that consists of two or more simple machines used together
Section 1: Work and Machines Lever – a bar that is free to pivot, or turn, about a fixed point. • There are three classes of levers: 1stclass lever – the fulcrumis between the effort and the resistance • Multiplies effort force and changes its direction • Examples: crow bars, teeter-totters 2nd class lever – the resistanceforce is between the effort force and the fulcrum • Multiplies force without changing direction • Examples: wheel barrows, doors 3rd class lever – the effort force is between the fulcrum and the resistance force • The effort force is always greater than the resistance force. MA < 1 • Examples: the fore-arm, fishing poles If the 3rd class lever has no mechanical advantage, why use one?
Section 1: Work and Machines Calculating the mechanical advantage of levers • Equation: or: • the distances are measured from the fulcrum to the point where the forces are acting Example: If the distance of the effort force is 3-m, and the distance of the resistance arm is 1-m, what is the mechanical advantage of the lever? Solution: Notice the distance units cancel. Remember, mechanical advantage is just a number.
Section 1: Work and Machines Pulleys • The two sides of the pulley are the effort arm and the resistance arm. • A fixed pulley changes the direction of the force only, it does not increase force • A moveable pulley will increase the effort • Block-and-tackle – a system of pulleys consisting of fixed and moveable pulleys. The block-and-tackle will multiply the effort force Wheel-and-axle – a machine consisting of two wheels of different sizes that rotate together Inclined plane (ramp) – a sloping surface that reduces the amount of force required to do work • The same amount of work is done by lifting a box straight up or by sliding it up a ramp. However, the ramp reduces the amount of force required by increasing the distance • Mechanical advantage of a ramp:, or: Example: Jessica uses a ramp 5-m long to raise a box to a height of 1-m. What is the mechanical advantage of the ramp? Solution
Section 1: Work and Machines Screw– an inclined plane wrapped around a cylinder Wedge– an inclined plane with one or two sloping sides Mechanical Efficiency (ME) • Recall that the amount of work done by the machine (work output) is always less than the work done on the machine (work input) • Mechanical Efficiency is the measure of how much of the work put into a machine is changed into useful output work by the machine • Because of friction no machine is 100% efficient. ME will always be less than 100% • Equation: , or: Example: John is changing a flat tire on his truck. He does 2,500J of work on the jack, while the jack does 2,100J of work on the car. How efficient is the jack? Solution
Section 2: Describing Energy Energy – the ability to cause change • Energy comes in different forms chemical, electrical, thermal, etc. • We will be looking at three (3) types of energy: kinetic, potential, and mechanical. • Kinetic Energy (KE) • KE is energy in a moving object • Anything that moves has kinetic energy • Kinetic energy depends of two things:1. the mass of the moving object2. the velocity of at which the object is moving • Equation for kinetic energy: • Unit for energy:
Section 2: Describing Energy Example: A ball, m = 1.5-kg, is rolling across the floor towards the door at 2 m/s. What is the KE of the rolling ball? Solution Important: Always square the velocity before you do any multiplication • Potential Energy • Potential energy – energy stored due to an object’s position • Three types of potential energy: • Elastic – PE stored by things that stretch or compressEx.: rubber bands, springs, pole vault poles • Chemical – PE stored in chemicals bondsEx.: nuclear weapons and fuels • Gravitational – PE stored by things that are elevatedEx.: fruit on trees, bouncing balls
Section 2: Describing Energy • The amount of potential energy can be determined mathematically. We will focus on gravitational PE • Equation for gravitational PE: Example: An apple, mass = 0.5-kg, is hanging from a branch 4.0-m above the ground. What is its gravitational PE? Solution
Section 3: Conservation of Energy • Mechanical Energy – the total amount of potential and kinetic energy in a system • Equation: mechanical energy = potential energy + kinetic energy, or: Example: An object held in the air has a gravitational PE of 480.0J. What is its kinetic energy if it has fallen two-thirds of the way to the ground? • Law of Conservation of Energy: Energy is neither created nor destroyed • On a large scale: total energy in the universe is constant • Consequence: energy can change form: potential kinetickinetic thermalchemical mechanical
Section 3: Conservation of Energy • Power – the amount of work done in a certain amount of time • Power is a rate • Equation for calculating power: • Units for Power: the Watt (W)1 watt is about equal to the power required to lift a glass of water from a table to your mouth Example 1: It took 20 seconds to move a refrigerator, You did 3,150 J of work in the process. How much power was required to move the refrigerator? Solution Example 2: It took you 1.5 s to lift a 10-kg box of the floor to a height of 1.0-m. How much work did you do on the box, and how much power was required to do this?Solution