Vector diagrams

*Vectors should be drawn tip-to-tail

*Put arrows on all vectors

*Resultant arrow goes toward last open arrow

*angle is measured from the starting point

a. Find the speed of the model airplane.

b. On the diagram, draw a vector that shows the resultant velocity of the plane.

c. At what angle is the plane moving relative to east?

Vector diagrams

*Vectors should be drawn tip-to-tail

*Put arrows on all vectors

*Resultant arrow goes toward last open arrow

*angle is measured from the starting point

a. Find the speed of the model airplane. 1.6 m/s to 1.7 m/s

b. On the diagram, draw a vector that shows the resultant velocity of the plane. 6.3 cm to 6.7 cm @ 23 to 27 degrees

c. At what angle is the plane moving relative to east? 25 ± 20

25

0 scale: 1.5 m/s = 6 cm so 1 cm =0.25 m/s

resultant is ≈ 6.5 cm = 1.63 m/s

Using pythagoreant theorem: (1.5 m/s)2 + (.7 m/s)2 = R2

R = 1.66 m/s

Motion graphs

d v a

slope

area

a.Find speed at 1.0 sec.

b. Find acceleration at 7 sec.

c. Find distance traveled from 6 - 8 sec.

Constant speed shapes uniform acceleration shapes

Motion graphs

d v a

slope

area

a.Find speed at 1.0 sec.

b. Find acceleration at 7 sec.

c. Find distance traveled from 6 - 8 sec.

Constant speed shapes uniform acceleration shapes

5 m/s

slope = 15-10 m/s

8 - 6 s

=2.5 m/s2

area = 20 + 5 = 25 m

20 m

5 m

Projectile Motion

*The horizontal motion is constant speed

*The vertical motion is accelerated at 9.8m/s2

*Complementary angles have same range

*Most time and height-- closest to 900

*Farthest range -- closest to 450

a. Find the horizontal component of the initial velocity.

b. Find the vertical component of the initial velocity.

c. What is the acceleration of the ball at its highest point?

d. What is the speed of the ball at its highest point?

e. What other angle would go the same horizontal distance if projected at 25 m/s?

f. Draw the trajectory of a soccer ball kicked at 25 m/s and an angle of 45 degrees on the diagram.

Projectile Motion

*The horizontal motion is constant speed

*The vertical motion is accelerated at 9.8m/s2

*Complementary angles have same range

*Most time and height-- closest to 900

*Farthest range -- closest to 450

a. Find the horizontal component of the initial velocity.

b. Find the vertical component of the initial velocity.

c. What is the acceleration of the ball at its highest point?

d. What is the speed of the ball at its highest point?

e. What other angle would go the same horizontal distance if projected at 25 m/s? 50 degrees

f. Draw the trajectory of a soccer ball kicked at 25 m/s and an angle of 45 degrees on the diagram.

Ax = A cosθ = 25m/s(cos 400) = 19 m/s

Ay = A sinθ = 25m/s(sin 400) = 16 m/s

9.8 m/s2

19 m/s

Freebody Diagrams

*Only draw forces on the diagram and NOT the net force

*Weight is the only force that MUST be in FBD

*Normal force if touching a solid surface, Friction if not frictionless

b

.

c

.

a.Draw FBD.

d. What is the net force acting on the sled?

Freebody Diagrams

*Only draw forces on the diagram and NOT the net force

*Weight is the only force that MUST be in FBD

*Normal force if touching a solid surface, Friction if not frictionless

b

.

c

.

a.Draw FBD.

d. What is the net force acting on the sled?

F

f

FF

N

Fg

Ax = A cosθ = 60N(cos 300) = 52 N

52 N

zero. There is no net force.

*Net forces cause masses to accelerate in the direction of the NET force.

a = Fnet

m

An ice skater applies a horizontal force to a 20.-kilogram block on frictionless, level ice, causing

the block to accelerate uniformly at 1.4 meters/second squared to the right. After the skater stops pushing

the block, it slides onto a region of ice that is covered with a thin layer of sand. The coefficient of

kinetic friction between the block and the sand-covered ice is 0.28.

a. On the diagram below, starting at point A, draw a vector to represent the force applied to the block by the skater. Begin the vector

at point A and use a scale of 1.0 centimeters = 5.0 newtons.

b. Calculate the magnitude of the force of friction acting on the block as it slides over the sand-covered ice.

[Show all work, including the equation and substitution with units.]

*Net forces cause masses to accelerate in the direction of the NET force.

a = Fnet

m

An ice skater applies a horizontal force to a 20.-kilogram block on frictionless, level ice, causing

the block to accelerate uniformly at 1.4 meters/second squared to the right. After the skater stops pushing

the block, it slides onto a region of ice that is covered with a thin layer of sand. The coefficient of

kinetic friction between the block and the sand-covered ice is 0.28.

a. On the diagram below, starting at point A, draw a vector to represent the force applied to the block by the skater. Begin the vector

at point A and use a scale of 1.0 centimeters = 5.0 newtons.

b. Calculate the magnitude of the force of friction acting on the block as it slides over the sand-covered ice.

[Show all work, including the equation and substitution with units.]

Since there's no friction on the ice

skater, then the net force will be the

applied force acting on the skater.

a = Fnet/m

1.4 m/s2 = F/20kg

F = 28 N

Ff = μFN = .28(20kg x 9.8m/s2) = 55 N

28N/5N/cm =5.6 cm

28 N

Inclined Plane

*Force of gravity is broken into components

*Normal force is perpendicular to surface

a. Draw a FBD labeling all forces.

b. Determine the force of friction.

c. Determine the normal force.

Inclined Plane

*Force of gravity is broken into components

*Normal force is perpendicular to surface

a. Draw a FBD labeling all forces.

b. Determine the force of friction.

c. Determine the normal force.

F

N

Fg

F

f

Ff = Fgsinθ= 98N sin200= 33.5 N

FN = Fgcosθ= 98N cos200= 92.1 N

Circular Motion

*Net Force and acceleration toward center

*velocity is tangent to circle

a. Calculate the centripetal force

acting on the car.

b. How long does it take the car to go around the track?

c. Draw acceleration and velocity vectors on the cart at the position shown.

Circular Motion

*Net Force and acceleration toward center

*velocity is tangent to circle

a. Calculate the centripetal force

acting on the car.

b. How long does it take the car to go around the track?

c. Draw acceleration and velocity vectors on the cart at the position shown.

Fc = mac = mv2/r

= 1.5 kg(4m/s)2

2.4 m

= 10 N

a

v

v = d/t = 2πr/t = 2(3.14)(2.4m) = 4 m/s

t

t= 3.77 s

Work and Energy

*Work equals change in energy

*Work requires force and motion

*Work is never done in uniform circular motion

b. How much total energy does the system have at A.

c. Find the speed of the rollercoaster at B.

d. How does the KE at C compare to the KE at B?

a.

Work and Energy

*Work equals change in energy

*Work requires force and motion

*Work is never done in uniform circular motion

b. How much total energy does the system have at A.

c. Find the speed of the rollercoaster at B.

d. How does the KE at C compare to the KE at B?

a.

The total mechanical energy is the same.

PE = mgh = (250kg +75 kg)(9.8m/s2)(20m) = 63,700 J = 6.4 x104 J

PEtop= KEbottom= 6.4 x104 J = 1/2mv2 =1/2(325kg)v2

v = 20. m/s

The KE at C is less than at B.

Springs

*Use F=kx when a force is given or a weight is hung on a spring.

*Use PEs=1/2kx2 when speed or height is given since it implies conservation of energy

is being used.

Springs

*Use F=kx when a force is given or a weight is hung on a spring.

*Use PEs=1/2kx2 when speed or height is given since it implies conservation of energy

is being used.

Fs= kx 6N = k(.04m) k =150 N/m

a

.

b

.

a

.

b

.

PEs = 1/2 kx2

PE = 1/2(150 N/m)(.05 m)2 PE = 0.19 J

PEs = PE g = mgh

0.19 J = 0.02 kg(9.8m/s2)(h)

h = 0.96 m

Momentum

*Momentum is a VECTOR

*Impulse = Change in momentum

*LAW of Conservation of Momentum

1.

3

.

A B A B20 m/s 10 m/s 10 m/s 15 m/s

5 kg 5 kg

2.

Before After

Momentum

*Momentum is a VECTOR

*Impulse = Change in momentum

*LAW of Conservation of Momentum

1.

3

.

A B A B20 m/s 10 m/s 10 m/s 15 m/s

5 kg 5 kg

2.

Before After

100 kgm/s

p = mv

+ B10 kgm/s = 50 kgm/s + B15 kgm/s =

100 + 10B = 50 + 15 B B = 10 kg

+ 12 kgm/s - 18 kgm/s = - 6 kgm/s

magnitude = 6 kgm/s

total p = 0

-1.2kg v + 1.8kg(2m/s) =0

v = 3.0 m/s

b.

c.

Electrostatics

*Only electrons can move to give a charge

*Electric field lines point away from positive charges toward negative charges

a. Find force between the charges.

b.

c.

Electrostatics

*Only electrons can move to give a charge

*Electric field lines point away from positive charges toward negative charges

a. Find force between the charges.

Fe = kq1q2/r2 = 8.99 x 109 N-m2/kg2 (8x10-19C)(4.8x10-19C/(1.2x10-4m)2

Fe = 2.4 x 10-19 N

inverse square law

Series Circuits

*Everything gets the same current

*Total current depends on total resistance

*One device goes out, all go out

a. Find resistor, R.

b.Find potential difference across 50 ohm.

c. Find total energy in one minute for the

circuit.

d. If another resistor is added in series,

what happens to the ammeter reading?

Series Circuits

*Everything gets the same current

*Total current depends on total resistance

*One device goes out, all go out

a. Find resistor, R.

b.Find potential difference across 50 ohm.

c. Find total energy in one minute for the

circuit.

d. If another resistor is added in series,

what happens to the ammeter reading?

Requivalent = 120 V/0.5 A = 240 ohms

240 Ω = 50Ω + R R = 190Ω

V = IR=0.5 A(50Ω) = 25 V

W = VIt =120V(0.5A)(60s)=3600J

The ammeter reading decreases.

Parallel Circuits

*Potential difference is same

*Total resistance decreases as more resistors are added

*Each resistor is independent of each other

a. Find ammeter reading.

b. Find resistor, R.

c. Find charge in A2 in 1 minute.

d. If another resistor is added in parallel, will

either ammeter change its reading?

Parallel Circuits

*Potential difference is same

*Total resistance decreases as more resistors are added

*Each resistor is independent of each other

a. Find ammeter 1 reading.

R1 = V/I1 3Ω=12V/I1 I1 = 4 A

b. Find resistor, R.

R2 = V/I2 = 12 V/1A = 12Ω

c. Find charge in A2 in 1 minute.

A2 = Itotal = q/t 5A = q/60 sec

q = 300 C

d. If another resistor is added in parallel, will

either ammeter change its reading?

Only Ammeter 2 will change and it will

increase since it measures the total current.

Ammeter 1 will stay the same since it

measures an individual current.

5A 1A

4AItotal = I1 + I2 5A = 4 A + I2

Magnetism

*Compasses point in the direction of the magnetic field*

*The North pole is attracted to the South pole of a magnet

*Magnetic field lines go away from North poles and toward South poles

outside of a magnet, but point toward North poles inside of a magnet

1.Draw the direction of the compass needle.

a. Which magnet exerts the greater magnetic force on the other?

b. Which exerts the greater gravitational force on the other?

2.

Magnets

*Compasses point in the direction of the magnetic field*

*The North pole is attracted to the South pole of a magnet

*Magnetic field lines go away from North poles and toward South poles

outside of a magnet, but point toward North poles inside of a magnet

1.Draw the direction of the compass needle.

a. Which magnet exerts the greater magnetic force on the other? Neither,

both exert the same force on each other according to Newton's 3rd law.

b. Which exerts the greater gravitational force on the other?

Neither, both exert the same force on each other.

2.

b.

c.

Waves

*Transfer energy without matter

*speed depends on medium and type of wave

*frequency depends on source of wave

a. Is this wave longitudinal or transverse?

d. Label a point in phase with P and label it I, and a point 1800 out of phase and label it

O.

P

b.

c.

Waves

*Transfer energy without matter

*speed depends on medium and type of wave

*frequency depends on source of wave

a. Is this wave longitudinal or transverse?

d. Label a point in phase with P and label it I, and a point 1800 out of phase and label it

O.

P

8m/2.5 waves = 3.2 m

0.6 m

I I

O O

Refraction and Reflection

*All angles are measured from the normal

*The angle of reflection equals angle of incidence

*Refraction only occurs for rays at an angle to the normal and when the ray

enters a medium with a different n- value

a. Measure angle of refraction

b. Calculate angle of incidence.

c. Draw in the incident and reflected rays.

Refraction and Reflection

*All angles are measured from the normal

*The angle of reflection equals angle of incidence

*Refraction only occurs for rays at an angle to the normal and when the ray

enters a medium with a different n- value

a. Measure angle of refraction 370 ±20

b. Calculate angle of incidence.

c. Draw in the incident and reflected rays.

n1sinθ1=n2sinθ2

1.33sinθ1 =1.66sin370

θ1= 490

49

049

0

answers may vary slightly

depending on angle of refraction

that was measured

a. In a mercury atom, as an electron moves from

energy level i to energy level a, a single photon is

emitted. Determine this photon’s energy, in joules.

b. Calculate the frequency of this photon and

identify it.

c. How many possible photon energies could be

emitted from an electron in level i?

Modern Physics

*Energy is absorbed when electrons are excited to higher energy levels and

emitted when electrons drop down toward ground level

a. In a mercury atom, as an electron moves from

energy level i to energy level a, a single photon is

emitted. Determine this photon’s energy, in joules.

b. Calculate the frequency of this photon and

identify it. look at chart in reference table

c. How many possible photon energies could be

emitted from an electron in level i?

Modern Physics

*Energy is absorbed when electrons are excited to higher energy levels and

emitted when electrons drop down toward ground level

Ephoton = Ei - Ef = -1.56 - (-10.38) =8.82eV

8.82eV x 1.6x10-19 J/1eV =1.4 x10-18 J

E =hf 1.4 x10-18 J = 6.63 x10-34J-s (f)

f = 2 x1015 Hz is Ultraviolet

8 levels to fall to ground state

8+7+6+5+4+3+2+1=36

b. What is the charge of an omega particle?

a. What types of matter are all of these particles?

c. What is the charge of a lambda particle?

d. How much energy would be released if a proton and antiproton annihilate each

other?

Standard Model

*Quarks are found in pairs or triplets and experience the strong nuclear force

*Leptons are solitary particles that do not experience the strong nuclear force

*Energy and mass can be converted into each other by E = mc2

b. What is the charge of an omega particle?

a. What types of matter are all of these particles?

c. What is the charge of a lambda particle?

d. How much energy would be released if a proton and antiproton annihilate each

other?

Standard Model

*Quarks are found in pairs or triplets and experience the strong nuclear force

*Leptons are solitary particles that do not experience the strong nuclear force

*Energy and mass can be converted into each other by E = mc2

baryons

-1/3e+ -1/3e+ -1/3e = -1e

+2/3e+ -1/3e + -1/3e = 0

E = mc2 = 2 (1.67x10-27kg)(3 x108 m/s)2

= 3 x10-10 J

proton and antiproton have same mass