Work and Energy Energy Chapter 5: Section 2

Learning Targets Identify several forms of energy Calculate kinetic energy for an object Distinguish between kinetic and potential energy Classify different types of potential energy Calculate the potential energy associated with an object’s position P4.1e, P4.3A, P4.3d, P4.3f

Kinetic Energy Kinetic energy is the energy of motion ◦ An object in motion - whether it is vertical or horizontal - has kinetic energy Kinetic energy depends on both velocity and mass ◦ Therefore, the kinetic energy of an object with mass (m) and velocity (v) is : KE = ½ mv 2

According to the equation above, kinetic energy and mass are directly proportional If a bowling ball and a volleyball are traveling with the same velocity, the bowling ball will have a greater kinetic energy because it has a greater mass

KE = ½ mv 2 Kinetic energy of an object is also directly proportional to the square of its velocity. ◦ A 55 kg person running with a velocity of 5 m/s would have four times the kinetic energy of a person running with a velocity of 2.5 m/s

Units of Kinetic Energy Kinetic energy is a scalar quantity because it does not have a direction Like work, the SI unit of kinetic energy is the joule

Work-Kinetic Energy Theorem The net work done on a body equals its change in kinetic energy According to the work-kinetic energy theorem: W net = ∆KE

Work and Kinetic Energy An object’s speed increases if the net work is positive because the final KE is greater than the initial KE The object’s speed decreases if the net work is negative because the final KE is less than the initial KE

Potential Energy Potential energy is the stored energy of position possessed by an object Potential energy is associated with an object that has the potential to move because of its position ◦ A bow that is drawn ◦ A wrecking ball hanging from a crane Potential energy depends on an object’s interaction with its environment

Gravitational Potential Energy Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. ◦ The energy is stored as the result of the gravitational attraction of the Earth for the object.

Calculating Gravitational PE Gravitational potential energy is dependent on both mass and height Therefore, when free-fall acceleration is constant the formula for GPE is: PE g = mgh ◦ Both mass and height have a direct relationship with gravitational potential energy ◦ The SI unit for PE is the joule

Height and GPE Gravitational potential energy is a result of an object’s position so it must be measured relative to some zero level ◦ Typically, the ground is considered zero ◦ When working on a lab table, you might assign that the position of zero height

Since the gravitational potential energy of an object is directly proportional to its height above the zero position, a doubling of the height will result in a doubling of the gravitational potential energy.

Suppose you drop a ball from a second-floor roof and it lands on a first-floor roof. Does the ball still have gravitational potential energy? ◦ If h is measured from the ground then gravitational potential energy is not zero because the ball is still above the ground ◦ If h is measured from the first floor roof, the PE is zero when the ball lands on the roof

Elastic Potential Energy Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing ◦ Example: A spring or the stretched strings of a guitar The amount of energy depends on the distance the spring is compressed or stretched from relaxed length

Equation For Elastic PE PE elastic = ½ kx 2 k = spring constant x = distance compressed or stretched For a flexible spring, the spring constant is small For a stiff spring, the spring constant is large ◦ Spring constants have units of N/m

Chemical Potential Energy Chemical potential energy is the energy stored in food or fuel that is transformed into work ◦ Energy is stored in the bonds between atoms ◦ The stronger the bonds, the less chemical energy