Energy, Work and Simple Machines Unit 8

Vocabulary Work Energy Kinetic energy Work-energy theorem Joule Power Watt Machine Effort force Resistance force Mechanical advantage Ideal mechanical advantage Efficiency Compound machine

Objective: Describe the relationship between work and energy. Newton’s Laws: used to analyze motion Force and mass were used to determine acceleration Acceleration information was used to determine velocity or displacement for a time interval

New Approach to Analyzing Motion The work-energy approach Analyze the affect that work has upon the energy of a system (or system of objects) Determine the resulting velocity or height of the object from the energy information Work-energy theorem: when work is done on an object, the result is a change in kinetic energy. W = ∆KE

What is work? when a force acts upon and object and causes its displacement 3 ingredients to work: Force Displacement Cause For a force to qualify as having done work, there must be a displacement and the force must be the cause of the displacement.

Examples of work….

Work or Not! Consider the following examples. Decide if they represent work or if work is being done. A teacher pushes on a wall and becomes tired. A book falls off a table and free falls to the floor. A rocket accelerates through space.

Energy A massive, fast-moving vehicle can do damage to the objects around it. A baseball hit at a high speed can rise high into the air. What property of an object can produce a change in the object itself or the world around it? Answer: Energy. Both the vehicle and the baseball possess energy that is associated with their motion. This is known as kinetic energy and represented by the symbol KE.

Mathematically speaking…. W = Fd (work is equal to the product of Force and displacement) KE = ½ mv2 W = ∆KE

The relationship between work done and the change in energy that results was established by 19th century physicist James Prescott Joule. To honor him, the unit of energy is called a joule (J) Example: if a 2kg object moves at 1m/s, it has a kinetic energy of 1kg·m2/s2 or 1 Joule.

Review: What is a system? A system is the object of interest The external world is everything else Example: one system might be a box in a warehouse and the external world might consist of you, Earth’s mass and anything else external to the box.

Direction of energy transfer can go both ways. Through the process of doing work, energy can move between the external world and the system. Direction of energy transfer can go both ways. If external world does work on the system, then W is positive and the energy of the system increases If the system does work on the external world, then W is negative and the energy of the system decreases.

Calculating Work… W=Fd (work is measured in joules too. One joule of work is done when a force of 1N acts on an object over a displacement of 1m. ) Holds only for constant forces exerted in the direction of motion What happens if the force exerted is perpendicular to the direction of the object? Consider a planet in circular orbit. The force is perpendicular to the direction of motion. A perpendicular force does not change the speed of the planet only its direction. Consequently the gravitational force does not work on the planet. The kinetic energy remains constant as well. If KE = 0 (constant) then W=0. F and d are at right angles.

Force exerted at an angle A force exerted in the direction of motion does an amount of work A force exerted perpendicular to the motion does NO work. What work does a force exerted at an angle do?

Consider a force applied to a car at an angle. The net force is doing the work is the component That acts in the direction of the displacement. Fx Fy What work is done by the person pushing the car? Any force can be replaced by its components. If we consider a 125 N force exerted In the direction of the person’s arm, it has 2 components. The magnitude of the Horizontal component is Fx and the vertical component is Fy . Calculate both components. X: Y: The negative sign on the Y component indicates that it is downward. The horizontal force In the x direction is responsible for the displacement of the car and therefore is Responsible for the work done.

Work (angle between force and displacement) W = Fdcosθ Work is equal to the product of force and displacement, times the cosine of the angle between the force and the direction of the displacement.

Consider the car in the previous example Consider the car in the previous example. Other agents exert forces on the pushed car. Earth’s gravity (downward) The ground (upward) Friction (horizontal, opposite the direction of motion) Which forces produce work?