Vector diagrams *Vectors should be drawn tip-to-tail *Put arrows on - - PDF document

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

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 F F 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 B

20 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 B

20 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

4A

Itotal = 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

• utside 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

• utside 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 49 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
• ther?

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
• ther?

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