MECHANICAL ENERGY

EQ: What type of energy describes the motion of a

system?

• The word energy is used in many different ways in everyday speech.

• Some fruit-and-cereal bars are advertised as energy sources. Athletes use energy in sports.

• Companies that supply your home with electricity, natural gas, or heating fuel are called energy companies.

The Many Forms of Energy

• Scientists and engineers use the term energy much more precisely.

• Work causes a change in the energy of a system.

• That is, work transfers energy between a system and the external world.

The Many Forms of Energy

• When work is done on a system, the energy of that system increases.

• On the other hand, if the system does work, then the energy of the system decreases.

The Many Forms of Energy

Mechanical energy is the energy that is possessed by an object due to its motion or due to its position.

The total mechanical energy of a system is the sum of the PE and KE of a system

Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position

What is causing the ball to move in the other direction? What would happen to the one side of the ball if the other ball was lifted higher to begin the motion? Why?

https://www.youtube.com/watch?v=OuA-znVMY3I

Hmm?!

https://www.youtube.com/watch?v=GQGYXuSjo-E

https://www.youtube.com/watch?v=OuA-znVMY3I

Kinetic energy exists whenever an object which has mass is in motion with some velocity. Everything you see moving about has kinetic energy.  The greater the mass or velocity of a moving object, the more kinetic energy it has.

Formula:

KE = ½ m v2

Quantity Variable

Unit

Kinetic Energy

KE Joules (J)

mass m Kilograms (kg)velocity v Meters/second

(m/s)

Kinetic Energy Example

Silvana Cruciata from Italy set a record in one-hour running by running18.084 km in 1.000 h. If Cruciata’s kinetic energy was 694 J, what was her mass?

Example continuation Givens:Δx = 18.084 km = 1.8084 × 104 mΔt = 1.000 h = 3.600 × 103 sKE = 694 J

Unknown: mass

Equation(s):manipulated

Substitution: v =1.8084 × 104 m/3.600 × 103 s = 5.023 m/sm = 2(694)/(5.023)2 = 55.0127

Solution:m = 55.0 kg

Ability to do work by virtue of position or condition. In other words, the amount of work the object capable of doing based on its position.

A stretched bowA suspended weight

Potential Energy

Two Types of Potential Energy: Gravitational Potential Energy (GPE): The energy

associated with an object due to the object’s position relative to a gravitational source.

Elastic Potential Energy: The energy stored in a compressed or stretched spring.

Gravitational Potential Energy

Quantity Variable

Unit

Potential Energy

PE Joules (J)

Mass M Kilogram (kg)height ∆y Meters (m)gravity g Meters/second

(m/s2)

Formula:

PE = m g h

In 1993, Javier Sotomayor from Cuba set a record in the high jump by clearing a vertical distance of 2.45 m. If the gravitational potential energy associated with Sotomayor at the top point of his trajectory was 1.59 x 103 J, what was his mass?

Gravitational Potential Energy Example

m = 66.2 kg

Elastic Potential Energy

Quantity Variable

Unit

Potential Energy PE Joules (J)Spring constant k Newton/meter

(N/m)Distance compressed or stretched

x Meters (m)

Formula:

PEelastic = ½ kx2

A 70.0 kg stuntman jumps from a bridge that is 50.0 m above the water. Fortunately, a bungee cord with an unstretched length of 15.0 m is attached to the stuntman, so that he breaks his fall 12.0 m above the water’s surface. If the total potential energy associated with the stuntman andcord is 3.43 x 104 J,what is the force constant of the cord?

Elastic Potential Energy Example

Example continuation:Givens:m = 70.0 kg h = 12.0 mx = 50.0 m − 12.0 m − 15.0 m = 23.0 mPEg = 0 J at river levelPEtot = 3.43 × 104 Jg = 9.81 m/s2

Unknown: k

Equation(s):PEtot = PEg + PEelasticPetot = mgh + 1/2kx2 manipulated

•The change in gravitational potential energy of an object is equal to the amount of work needed to change its height•Therefore:

Work = DPEFd = mgh

•The KE of a moving object is equal to the work the object is capable of doing while being brought to rest•Therefore:

W = DKE Fd = ½mv2

A forward force of 11.0 N is applied to a loaded cart over a distance of 15.0 m. If the cart, which is initially at rest, has a final speed of 1.98 m/s, what is the combined mass of the cart and its contents?

Work-Energy Theorem Example

•Putting these two ideas together gives us the general Work-Energy Theorem:

If no change in energy occurs, then no work is

done. Therefore, whenever work is done, there is a

change in energy.

Closing Task•Show your knowledge of how kinetic and potential energy are converted from one form to the other by labeling the amount of KE and PE on the illustration at various points. Sketch it into your notebook