SPH 3UO LESSON PLANS

Text: Physics 11 (Addison-Wesley)

Work:
Conditions for physics work
1. A force must be exerted on an object
2. The object must be displaced by the force
3. Part of the force and the displacement must be in the same direction

ex. lifting a package
holding a package
holding a package while gliding on a frictionless skateboard
pushing a package along a rough surface
firing a rocket
spaceship coasting in space

In general work and displacement aren't in exactly the same direction
ex. pulling a wagon
                                F /\
                                 /O
                                /___\
                                   d
only the component of force in the direction of the displacement matters
                                F /\
                                 /O
                                /___\
                                 FcosO
work = (component of force in direction of /\d) x (/\d)

         W  = F cosO d
units (Nm) (N)       (m)
Note: 1 Nm = 1 J
work is a scalar (no direction)
work can be negative

eg. lowering a mass agaist gravity...W=FcosOd
            /\
             I F
           ***
             I
             I d
            \/

Example 1. A 150 g book is lifted from the floor to a shelf 2.0 m above.
Calculate the work done on the book.
Example 2: A force of 172 N is applied at an angle of 47^o while pushing a baby carriage 16 m along a sidewalk. How much work is done?
Example 3: A nurse holding a new-born 3.0 kg baby at a height of 1.2 m off the floor carries the baby 15 m a constant velocity along a hospital corridor. How much work has the nurse done on the baby?

Calculating Work Graphically...
In general, F might change in direction of magnitude or both.In this case the formula W= FcosOd does not work since there is no value for F or O
Plot a graph of F vs d then W is the area under the curve
ex.
   I   /
F I  /         W = (1/2)bh
   I/__________
    d
   I         __
   I__     I   I
F I    I__I   I    W = A + B + C
   I_a_b_c_I__
    d

Energy...the ability to do work
Energy has many forms...
1) rest mass energy
2) nuclear energy
3) gravitational potential energy
4) elastic energy
5) kinetic energy
6) chemical energy
7) sound energy
8) thermal energy
9) radiant energy
10) electrical energy

Energy cannot be created or destroyed
It can only be transformed to other forms
The total amount of energy in the universe is constant

Kinetic Energy...moving things have the ability to do work
ex. A ball will compress a spring and do work.
     The faster the ball is moving, the more work it can do.
     The heavier the ball, the more work it can do.
         E_K = (1/2) m    v²  
       units (J)     (kg)(m/s)

energy is measured in J
energy is a scalar

The energy of an object is determined by measuring how much work it can do
Example 1: A softball travelling at 34 m/s has a kinetic energy of 98 J.
                 What is its mass?
Example 2: A 100 g cup falls and shatters on the floor.
                 When it hit the floor it had a kinetic energy of 5.0 J.
                 What was the cup's maximum velocity?
                 What happened to the 5.0 J of energy?
Example 3: Show that the unit for kinetic energy is a joule.

Gravitational Potential Energy
-energy that results from the position of an object
/\E_G = m g /\h
m = mass (kg)
g = acceleration due to gravity (9.8 m/s²)
/\h = change in height (m)
/\E_G = change in gravitational potential energy (J)

-no such thing as an absolute potential energy. It is always with reference to a starting height.
-depends only on /\h (path independent)
W = /\E

Example 1: A 20 kg box of groceries was lifted 0.5 m into a car.
                 What was the change in gravitational potential energy?
                 What was the work done on the box of groceries?
Example 2: The cart has a mass of 200 kg.
                  Find the gravititational potential energy at A copared to the ground.
                  Find the change in potential energy from B to C.
A
50 m      B
              25 m      C
                            10 m

Example 3: Show that the units for gravitational potential energy are joules.

Elastic Potential Energy
E_E= (1/2)k x²
k = spring constant (N/m)
x = distance from the natural position (m)
E_E= elastic potential energy (J)

Finding k for a spring...
k = F/x
Hang a known mass on a spring and measure how much it stretches.
k= mg/x
ex. the bigger the k the harder it is to stretch
Example 1: A spring has a constant of 320 N/m.
                 How much must this spring be compressed to store 50 J?
Example 2: A spring is stretched by 5 cm when a 100 g mass is hung on it.
                 What is the spring constant for this spring?
Example 3: show the units for elastic potential energy are joules.

Elastic Lab

Mass and Energy
Until 1905, it was believed that matter could not be created or destroyed
Recall: CH₄ + 2O₂ --> 2H₂O + CO₂
mass or reactants = mass of products
Einstein proposed that E = mc²
E = energy that appears (J)
m = mass that disappears (kg)
c = speed of light = 3 x 10⁸

Nuclear Fusion
2H + 2n^o --> He     In the sun
mass of reactants is greater than the mass of products
mass was lost...the lost mass appears as energy by E =  mc²
A little bit of lost mass show up as a lot of energy

Nuclear Fission...
n^o + ²³⁵U --> ²³⁶U --> Ba + Kr + 3 n^o (...nuclear weapons)
mass of reactants is greater than the mass of the products
mass is lost and appears as energy by E =  mc²

Aside: chemical reactions can release heat...Breaking chemical bonds releases energy but no mass is lost.

Example 1: If 1.0 g of a substance changes entirely into energy , how much energy is produced?
Example 2: If one megajoule of energy was created during a nuclear reaction, how much mass was converted into energy?
Example 3: Show that the equation E = mc² is dimensionally correct.

Other questions...
1. Find the amount of energy released in the fusion reaction when two protons, each with a mass of 1.673 X 10^-27 kg, combine with two neutrons, each with a mass of 1.675 X 10^-27 kg, to produce an alpha particle with a mass of 6.647 X 10^-27 kg.

2. Find the energy released in the following fission reaction:
n^o + U-235 --> Sr-90 + Xe-136 + 10n^o
Particle        Mass(x10^-27kg)
neutron         1.675
U-235        390.989
Sr-90         149.301
Xe-136       225.687

3. Every second in our sun 4 x 10⁹kg of mass disappears and changes into energy. If the mass of the sun is 2 x 10³⁰kg how long do we have until the "death" of our sun?

4. When in 1939 Enrico Fermi found that uranium was fissionable he commented that it was just a matter of luck that he had not discovered it five years earlier. He also said that the world was fortunate that he hadn't discovered it five years earlier in light of events in Europe around that time. Do some research and explain why he felt that way.

Energy Transformation
1. In a spring... Figure 4.30, page 167
a) system has no energy
no kinetic energy
no potential energy (h = 0 at table top)
no elastic potential (spring is not stretched)
b) you do work on the mass, maybe 10 J
system has 10J stored as gravitational potential energy of the mass
c) mass swings down, gains some kinetic energy, gains some elastic energy, losses some gravitational potential energy...
but E_tot=E_E+E_G+kinetic energy = 10 J
d) mass reaches the bottom, no kinetic energy, maximum elastic energy, small potential energy but E_tot=E_E+E_G+kinetic energy = 10 J
e) mass swings up, gains kinetic energy, gains E_G, lossesE_E, but E_tot = 10 J
f) mass at the top, kinetic energy = 0, E_E = 0, all P_E,   E_tot = E_G = 10

Machines: a machine is a device that enables us to do work more easily
Examples of simple machines
1) lever
2) incline plane
3) pulley
4) wedge
5) wheel and axle
6) jackscrew

Actual mechanical advantage...
AMA = load force/applied force = F_G/F_A
Ex. It takes 100 N to lift a box...using an incline plane a force of 70 N can move the box
AMA = 100 N/70 N = 1.4

Efficiency = useful work done/actual work done x 100%
table 5.1 --> incandescent light = 2%
                     fluorescent light = 20%

Levers...load (must be lifted), fulcrum (pivot point), F_A is force applied
First class lever has fulcrum between load and F_A
Second class lever has load between fulcrum and F_A
Third class lever has force between fulcrum and load
         Torque (T) = distance to fulcrum x force applied
units   Nm              m                               N

Incline Plane example
The work to drag a 50 kg box to the top of a 3.0 m high ramp is 2000 J.
Calculate the efficiency of the ramp.

Lever example
It takes 60 N of force to open a certain door when pushing from a point 1 m from the hinges.
How much force would be required if you were to push from a point that is only 0.75 m from the hinges?

Pulleys: ideal mechanical advantage (IMA) - count the number of strands pulling up on the load
Ex. figure 5.9...a) IMA=1, b)IMA=2
AMA (actual) is always slighty less than the IMA (ideal)
Each pulley adds some friction so some energy is lost

Power: the rate at which work is done
Power (J/s) = work (J)/time (s) = energy used (J)/time (s)
P = W/t = E/t
1 J/s = 1 W (Watt)
Power is a scalar
Power = W/t but W = Fd

P = Fd/t  but v_av = d/t
           P =    F   v_av
units  (W)      (N) (m/s)

Thermal Energy and Heat...
Thermal Energy: the sum of the kinetic and potential energies of all the molecules of all the molecules of a substance.
E_Thermal = E_kinetic + E_potential

Thermal Energy                                      Reason
hot object > cold object                           molecules are moving faster (more kinetic energy)
steam @ 100 ^oC > water @ 100 ^oC          molecules are farther apart (more potential energy)

Heat: is the transfer of thermal energy.
         If the thermal energy of a substance increases then heat has been added.
Factors affecting heat:
1) Mass is directly proportional to heat.
    It takes twice as much heat to boil 2 kg of water as it does to boil 1 kg of water.
2) Temperature change is directly proportional to heat.
    It takes twice as much heat to change 1 kg of water by 10 ^oC as it does to change by 5 ^oC.
3) Type of material: it takes more heat to raise the temperature of oil by 1^oC than water.

             c     =   Q / m  /\T
units J/kg^oC       J    kg  ^oC or K

-c is specific heat capacity...it is the amount of heat required to raise the temperature of 1 kg by 1^oC.
-things with a large c need a lot of heat to change T and cool down slowly.

Table 5.4 , page 195 *ice, water, water vapour

note: water = 4200 J/kgK, sand = 800 J/kgK, explaining why sand is hotter during the day and water is hotter at night.

Hot water
Q_lost = mc/\T
         =(0.5 kg)(4200 J/kg^oC)(T_f - T_i)
         =(0.5 kg)(4200 J/kg^oC)(90^oC - T_f)

Cold water
Q_gained = mc/\T
              =(0.2 kg)(4200 J/kg^oC)(T_f - 20^oC)
Q_lost = Q_gained
(0.5 kg)(4200 J/kg^oC)(90^oC - T_f) = (0.2 kg)(4200 J/kg^oC)(T_f - 20^oC)
45^oC - 0.5 T_f = 0.2 T_f - 4^oC
49^oC = 0.7T_f
T_f =  70^oC

Example 1: What will be the final temperature of 200 g of water at 30^oC when 12 600 J of heat is added to it?
Example 2: If 500 g of water at 90^oC is mixed with 200 g of water at 20^oC, calculate the final temperature of the mixture.

Latent  Heat:
A temperature change ===> heat is transferred
Heat is transferred =X=> a temperature change

Heat can be added to a substance with no change in temperature. This is called "latent" heat.
l (latent heat, J/kg)= Q (heat, J)/ m (mass, kg)

Latent heat of fusion: l_f
-the amount of heat required to melt 1 kg of a substance
Latent heat of vaporization: l_v
-boiling
Table 5.6, note: it takes 333 kJ to melt 1 kg of ice.