Energy Energy- The property of an object that

allows it to produce change in the environment or itself.

Types of energy Thermal Chemical Solar Nuclear Geothermal Hydroelectric Wind

Energy Kinetic Energy- The energy of an object

resulting from motion. K = 1/2 mv2

Work - The process of changing the energy of a system

W = Fd Work is a scalar quantity Work-Energy Theorem ∆K = W A unit of energy/work = N•m = Joule (J)

Energy How much work is done in lifting an object

with a mass of 20 kg to a height of 3 meters?

m = 20 kgd = 3 m

F = mg = (20 kg)(9.8 m/s2) = 196 N

W = Fd = (196 N)(3 m) = 588 N•m = 588 J

Energy How much work is done in pulling a pail

up a well by turning a crank 40 times with a radius of 80 cm with a force of 50 N?

F = 50 Nr = .8 mn = 40

W = Fd W = (40)(50 N)(2π)(.8 m) = 10048 J

Energy Power- The rate of doing work P=W/t J/sec = watt

A box weighing 200 N is lifted a distance of 12 m in 10 seconds.Find the work and power.

W = F d

W = (200 N)(12 m) = 2400 J

P = W/t

P = 2400 J / 10 sec = 240 W

Energy

A force of 70 N is applied to a lawnmower at an angle of 30°. The lawnmower is moved 50 meters. How much work is done?

F = 70 Nd = 50 m

30º

70 N

W = Fd = (F cos )d W = (70 N) (cos 30°)(50 m)

W = 3031 J

Energy Simple Machines- A device that

changes the magnitude or the direction of a force needed to do the work

1. Pulley2. Lever3. Wheel and Axle4. Inclined Plane5. Screw6. Wedge

•Fr Resistance Force •Fe Effort Force •dr Resistance distance•de Effort Distance

Fe

Fr

Lever

Fe

Fr

Fe

1/2 Fr

1/2 Fr

Fe

Fr

Fe

Fr

Fe

Fr

Energy Mechanical Advantage (MA) - The ratio of

the resistance force to the effort force. MA = Fr/Fe

Ideal Mechanical Advantage (IMA) - The ratio of the effort distance to the resistance distance.

IMA =de/dr

Energy Efficiency - The ratio of the work output to the

work input

Efficiency (%) = WO/Wi x 100 = MA / IMA x 100

An efficient machine has an MA almost equal to its IMA. No machine has an efficiency greater than 100%

A team of movers uses an inclined plane 3 meters long to move apiano weighing 3000 newtons over a doorstop .27 m high by applying a force of 500 newtons.Calculate the MA, IMA, and the efficiency.

Fr = 3000 NFe = 500 Ndr = .27 mde = 3 m

MA = Fr/Fe = 3000 N/ 500 N = 6

IMA = de/dr = 3 m/.27 m = 11.1

Eff = MA/IMA = 6 / 11.1 = 54% or

Eff = WO/Wi = (3000 N)(.27m)/(500 N)(3m) = 54%

Energy

A force of 225 N is displaced 7.35 m which moves a weight of 1340 N to a height of .975 mCalculate the MA, IMA, and the efficiency. Fr = 1340 N

Fe = 225 Ndr = .975 mde = 7.35 m

MA = Fr/Fe = 1340 N/ 225 N = 5.95

IMA = de/dr = 7.35m/.975m = 7.54

Eff = MA/IMA = 5.95 / 7.54 = 79% or

Eff = WO/Wi = (1340 N)(.975m)/(225 N)(7.35m) = 79%

Energy

The efficiency of a lift is 72.5% What work is needed if a mass of 200 kg is displaced 5.65 m?.

m = 200 kgFr = 1960 Ndr = 5.65 m

Eff = WO /Wi

Wi = WO / Eff

Wi = (1960 N)(5.65 m)/.725

Wi = 15274 J

Energy

A resistance of 475 N is displaced .623 m by an effort force of 178 N. The efficiency of the machine is 85%. What is the displacement of the effort force?

Eff = WO /Wi = (Fr)(dr)/(Fe)(de)

de = (Fr)(dr)/(Fe)(Eff)

de = (475 N)(.623 m)/(178 N)(.85)

de = 1.96 m

Fr = 475 NFe = 178 Ndr = .623 mEff = .85

Energy

Observations About Seesaws

A balanced seesaw can remain horizontal A balanced seesaw rocks back and forth easily Two equal-weight children balance a seesaw Two unequal-weight children don’t balance But moving the heavy child inward helps

Physics Concept

• Rotational Inertia– A body at rest tends to remain at rest.– A body that’s rotating tends to continue rotating.

A note on positive/negative work If force is parallel to displacement

work is positive If force is antiparallel to

displacement work is negative If force is perpendicular to

displacement work is zero.

Physical Quantities for rotational motion

• Angular Position – an object’s orientation (angle with respect to reference, i.e. horizontal

• Angular Velocity – its change in angular position with time

• Torque – a twist or spin (more later)

Angular rotation or

Angular position

• SI unit of angular rotation is the radian

• One radian is 180°/57.3°

• Rotation requires an axis of rotation

Angular velocity

• SI unit: radians per second or just 1/sec

• An other unit: rotations per minute (not an SI unit).

• Measure of how fast an object spins

• Angular velocity is a vector!

• Use right hand rule to determine direction of vector• Align right thumb with axis

• Align fingers with rotational movement

• Thumb points into direction of angular velocity vector

Angular velocity is a vector

Right-hand rule for determining the direction of this vector.

• rotates through the same angle,

• has the same angular velocity,

• has the same angular acceleration.

Every particle (of a rigid object):

Newton’s First Lawof Rotational Motion

A rigid object that’s not wobbling and that is free of outside torques rotates at a constant angular velocity.

When an object is rotating freely (no fixed axis), it rotates about its center of mass

Center of mass

Center of Mass

• The point about which an object’s mass balances

• A free object rotates about its center of mass while its center of mass follows the path of a falling object

How do we start something spinning???

We have to apply a torque to it• We need a

- pivot point

- lever arm

- applied force

Torque = force x lever arm

FrLever arm is perpendicular to applied force

Torque is a vector

It has a direction and a magnitude

Use the right hand rule to figure out the direction of the torque

- Thumb is torque,

- Index finger is lever, r

- Middle finger is Force, F

Moment of inertia

• The moment of inertia is a measure of an object’s rotational inertia, its resistance to change in angular velocity

• Analogous to mass (translational inertia)

• Moment of inertia depends on

• mass of object

• and mass distribution (where the mass sits with respect to axis)

• the axis about which the axis rotates

Which object is harder to rotate??

Physical Quantities

Angular Position – an object’s orientation Angular Velocity – its change in angular position

with time Torque – a twist or spin Angular Acceleration – its change in angular

velocity with time Moment of Inertia – measure of its rotational

inertia

Newton’s Second Lawof Rotational Motion

The torque exerted on an object is equal to the product of that object’s moment of inertia times its angular acceleration. The angular acceleration is in the same direction as the torque.

Torque = Moment of Inertia · Angular Acceleration

I

Physics Concept

• Net Torque– The sum of all torques

on an object.– Determines that object’s

angular acceleration.

1 m

Torques are equal (40 kg)(1 m) = x (1 m)The mass of the plank is 40 kg.

Beth has noFriends, she Has to teetertotter by herself

Summary: Angular and linear quantities

I

Angular position (angle):

Torque:

Linear motion Rotational motion

maF

Position: x

Force:

Velocity: v Angular velocity:

Acceleration: a Angular Acceleration:

Mass: m Moment of inertia: I

Momentum: mv Angular Momentum: mvr

Law of Conservation of Angular Momentum

In a closed system, angular momentum is conserved

(mvr)before = (mvr)after

Kinetic Energy – Energy of an object due to motion

Potential Energy – Energy of an object due to position

K = ½ mv2

•Gravity•Spring•Battery•Chemical Bonds

Anything that can be converted to energy

Ug= mgh

Energy

Energy

A car with a mass of 1000 kg moves with a velocity of 20 m/s.What is its kinetic energy?

m = 1000 kgv = 20 m/sK = ½ mv2

K = ½ (1000 kg)(20 m/s)2 = 200000 kg m2/s2 = 200000 J

EnergyA roller coaster of mass 3000 kg goes from point A to point B topoint C.

A

B

C33 m

10 m

15 m

a. Find the potential energy at A.

b. Find the potential energy at C.

Energy

A

B

C33 m

10 m

15 m

UA = mgh = (3000 kg)(9.8 m/s2)(33 m) = 970,200 J

UC = mgh = (3000 kg)(9.8 m/s2)(15 m) = 441,000 J

Energy

Law of Conservation of Energy – The total amount of energy in aclosed system is constant.

Mechanical Energy E = K + Ug

Conservation of Mechanical EnergyKbefore+Ug before = Kafter+Ug after

10 N

10 N

10 N

20 m

10 m

KE = 0 JPE = 200 J

KE = 100 JPE = 100 J

KE = 200 JPE = 0 J

EnergyA ball with a mass of 20 kg falls from a roof 10 meters high.

a. What is the potential energy?b. What is the kinetic energy of the ball when it reaches the ground?c. What is the speed of the ball when it hits the ground?

a . Ug = mgh = (20 kg)(9.8 m/s2)(10 m) = 1960 J

b. Kbottom= Ug top Kbottom = 1960 J

c. K = ½ mv2

m

2Kv

kg 20

J 1960*2v m/s14v

Elastic Collision Collision in which the total kinetic energy of twoobjects is the same after the collision as before.

Inelastic Collision Collision in which some of the kinetic energyis changed to another form of energy.

Energy