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Chapter 5 Work and Energy. Chapter 5: Work and Energy. 5.1 Work Done by a Constant Force 5.2 Work Done by a Variable Force 5.3 The Work-Energy Theorem: Kinetic Energy 5.4 Potential Energy 5.5 The Conservation of Energy 5.6 Power. 5.1 Work Done by a Constant Force.
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Chapter 5: Work and Energy 5.1 Work Done by a Constant Force 5.2 Work Done by a Variable Force 5.3 The Work-Energy Theorem: Kinetic Energy 5.4 Potential Energy 5.5 The Conservation of Energy 5.6 Power
5.1 Work Done by a Constant Force Definition: Work done by a constant force is equal to the product of the magnitudes of the displacement and the component of the force parallel to the displacement.
5.1 Work Done by a Constant Force • W = (F cosӨ)d, where • F is the magnitude of the force vector • d is the magnitude of the displacement vector • Ө is the angle between the two vectors (Warning – this angle is not necessarily measured from the horizontal) • When the angle is zero, cos Ө = 1, and W = F·d • When the angle is 180°, cos Ө = -1 and W = - F·d (yes, negative work!) • example: the force of brakes to slow down a car. • Although force and displacement are vectors, work is a scalar quantity. • The SI unit of work is the N·m, which is called a joule (J).
5.1 Work Done by a Constant Force For a constant force in the same direction as the displacement, W = Fd. For a constant force at an angle to the displacement, W = (FcosӨ) d If there is no displacement, no work is done: W = 0.
Homework for Section 5.1 • See Handout provide in class.
5.6 Power A common British unit of power is the horsepower (hp) and 1 hp = 746 W.
5.6 Power Example 5.11: A 1500 kg car accelerates from 0 to 25 m/s in 7.0 s. What is the average power delivered to the car by the engine? Ignore all frictional and other losses.
Homework for Power • See handout
Energy • Energy is the capacity of a physical system to perform work. • Energy exists in several forms such as heat, kinetic or mechanical energy, light, potential energy, electrical, or other forms. • The SI unit of energy is the joule (J) or newton-meter (N * m). The joule is also the SI unit of work.
Law of Conservation of Energy • According to the law of conservation of energy, the total energy of a system remains constant, though energy may transform into another form. • Two billiard balls colliding, for example, may come to rest, with the resulting energy becoming sound and perhaps a bit of heat at the point of collision.
Basic Energy Model • Within a system, energy can be transformed between various forms. • Example #1: In a pendulum or swing (with the absence of frictional forces) Potential Energy Kinetic Energy Potential Energy • Example #2: Potential energy of oil or gas is changed into energy to heat a building. • In a closed system, the total energy in a system is constant and only transforms from on form of energy to another.
Basic Energy Model • In an open system (most systems are open), energy can be transferred into and out of a system in 2 ways: • Work: The transfer of energy by mechanical forces. • Example: a golfer uses a club and gets a stationary golf ball moving when he or she hits the ball. The club does work on the golf ball as it strikes the ball. Energy leaves the club and enters the ball. This is a transfer of energy. • Heat: The non-mechanical transfer of energy from a hotter object to a cooler object. • Example: Brake on a car creating heat while stopping and the area around the brakes getting hot.
I. Kinetic Energy Kinetic Energy – Energy of motion KE = K = ½ mv2 K = kinetic energy (Joules – J) m = mass (kg) v = velocity (m/s) Note: KE cannot be negative, because… • You cannot have a negative mass • Velocity is always squared
II. Elastic Potential Energy • Elastic potential energy is potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. • It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched.
II. Elastic Potential Energy PEe = Us = ½ kx2 PEe & Us = Elastic potential energy = Joules (J) k = spring constant (measures how stiff and strong the spring is) = N/m x = displacement of the spring from the rest or equilibrium position. (m) Note: PEe or Us cannot be negative because… • k cannot have a negative value • x is squared
II. Elastic Potential Energy A child pulls back horizontally on a rubber band that has an unstretched length of 0.1 m and it stretches to a length of 0.25 m. If the spring constant of the rubber band is 10N/m, how much energy is stored in the spring?
III. Gravitational Potential Energy • GPE is the energy associated with a gravitational field like the one we live in on Earth. AKA – Energy of position PEg = U = mgh PEg or U = gravitational potential energy – Joules (J) m = mass (kg) g = acceleration due to gravity (m/s2) h = height above ground (m) Note: GPE can be negative, but only if the object is below the horizontal line of the coordinate plane.
III. Gravitational Potential Energy A 10.0 kg object is moved from the second floor of a house 3.00 m above the ground to the first floor 0.30 m above the ground. What is the change in gravitational potential energy?
5.4 The Work-Energy Theorem: Potential Energy: Check for Understanding
5.4 The Work-Energy Theorem: Potential Energy: Check for Understanding
5.4 The Work-Energy Theorem: Potential Energy: Check for Understanding
5.4 The Work-Energy Theorem: Potential Energy: Check for Understanding Or, use opp = hyp (sin 30) = 0.5 m
Variable Forces: Spring Forces & Energy AP Physics I
I. Spring Forces Back and forth motion that is caused by a force that is directly proportional to the displacement. The displacement centers around an equilibrium position.
