Physics Test Unit 3

Energy of motion

• translational kinetic energy

• K = ½ * mv²

• depends of reference frame (observer’s view)

Hooke’s Law

Fs = -k * delta x

• If there is friction, the work done by friction reduces the kinetic energy:

• If there is friction, the work done by friction reduces the kinetic energy:

Kfinal=Kinitial+Wspring+WfrictionKfinal​=Kinitial​+Wspring​+Wfriction​

Work

• amount of mechanical energy transferred into or out of system

• Constant force = W = Fdcostheta

• Theta = angle between direction of F and d

Work done by a conservative force in system

• independent of path of object

• Depends on initial and final configurations

• If displacement 0, zero work done and change in potential energy is zero.

Nonconservative force examples

• force of friction and force of air resistance (also called drag force)

Work done by a nonconservative force

• Does depend on the path

Displacement under Fcostheta vs. x graph

• equals work

3 types of mechanical energy

• kinetic energy

• Gravitational potential energy

• Elastic potential energy

Potential energy

• energy stored in a system due to positions of objects in system

Gravitational potential energy in constant gravitational field equation

Pg = mgh

change in gravitational potential energy in constant gravitational field

Delta Ug = mg * delta y

Vertical height above horizontal zero line

• h or y

Symbols for potential energy

PE and U

Potential signs of PE and KE

• PE can be negative (b/c h can be negative)

• KE can’t be negative

Ug between two objects w mass

• - (Gm1m2)/r

• G is gravitational constant

• R is distance between centers of mass of the two objects

Ug = 0

• where both objects are infinitely far away from one another (r = infinity)

• Why general form of Ug is always negative

Gravitational constant

G = 6.67 × 10^-11 (N*m²)/kg²

Elastic potential energy

PEe = Ue = ½ k(delta x)²

• energy stored in a mass-spring system

• Ue can’t be negative

Mechanical energy of a system

• some of systems K, PEg, and PEe

System w one object

• can only have kinetic energy

Conservation of energy

• any changes to the types of energies in a system are balanced by equivalent changes of other types of energies in the system or by a transfer of energy into or out of the system.

When total mechanical energy remains same

ME = ME

• zero net work done on system and zero work done by nonconservative forces

Work-Energy Principle

• net work equals change in kinetic energy principle

• Wnet = delta K

• Can be used when work is done by nonconservative forces on system

Power

• rate at which energy changes with respect to time, by either being transferred into or out of the system or converted from one type of energy to another within a system

• Rate at which wrk is done on a system

Average power formula

Pavg = delta E/delta t = W/delta t

Instantaneous Power

Fvcostheta

• v is instantaneous velocity of system or object

F parallel

• Fcostheta

Power units

Watts, (kg * m²)/s³

Examples of conservative force

• gravity force, spring force

Energy definition

• ability to do work (scalar) in joules

Internal energy

• heat energy that causes an increase in the temp of te system

Work done by friction

• Ffriction*d*costheta

Work energy Principle

• Ui + Ki + Wnc = Uf + Kf

Work energy theorem

• net work done on an object is equal to its change in kinetic energy

• Wnet = delta K = KEf - KEi

• Wnet = ½ *mvf² - ½ *mvi²

In system with no earth

There is no potential energy, just kinetic