Download Final Review PHYSICS40Smay 2015

Year End Review
PHYSICS 40S
Teacher: Mr. Andrew Hiebert
Once this review is done well in advance …
it is also highly recommended to:
a) Read through your notes, and make condensed notes of
the key concepts on cue cards.
b) Practice “redoing” the archetypal questions given as
examples in the notes.
c) Go through your tests and make sure you could redo each
of the questions with the correct work.
d) Create your own practice exams, and then do them. You
may wish to exchange practice exams with a peer for extra
practice.
e) REMEMBER:
Come for help as soon as you have trouble.
Getting help ‘last minute’ is often not as effective as
getting help ‘well in advance’ of the final exam.
1
2
Physics 40S
Comprehensive Exam Review
Vectors
1.
Add the following force vectors and express the resultant in standard form:
F1 = 300.0 N, at 37o
F2 = 400.0 N, at -60 o
[ANS= 469.8 N down69oright]
2.
What is the force that could cause equilibrium with the two vectors in problem #1?
[ANS= 469.8 N up 69oleft]
3.
A plane flies 20.0m [S15oW], then 30.0 m [E], and finally 110. m [N40 oE]. Find the
plane’s final displacement using the component method, given the vector diagram
below. [ANS = 116N (N56oE)]
4.
Tarzan swims across a river at a speed of 3.0 m/s, pointing his body [E40oN] into the
current, which is flowing at 2.0 m/s [W]. Will Tarzan end up further upstream (against
current) or downstream (with current)? Justify your answer by calculating the vx and vy
components and explaining. [ANS =0.0716 m/s E]
5.
Given v1 = 30.0 m/s [S10oW], and v2 = 5.00 m/s [S30oE], representing a ball hitting a
wall, find the change in velocity, Δv (v2 – v1), of the ball. Draw a vector diagram, and
then use the component or trig. method to solve.
Show that the answer is equal to 26.4 m/s [E73oN]
6.
A 200.0-kg log is pulled up a ramp by means of a rope that is parallel to the surface of
the ramp. The ramp is inclined at 30° with respect to the horizontal. The coefficient of
kinetic friction between the log and the ramp is 0.900 and the log has an acceleration of
0.400 m/s2. Find the tension in the rope. [ANS Ft=2590N uphill]
7.
Determine the two independent components for the following vectors using trigonometry then determine the
magnitude of each. [ANS (#1) 25.7m/s up, 146m/s right; (#2) 50.6N down, 139N left]
1.
148 m/s
2.
o
E10 N
θ
θ
148 m/s W20oS
3
PROJECTILE MOTION
1.
If a ball is fired vertically upward off of a stationary cart, draw it’s trajectory and say where it will land relative to
the cart.
2.
If a ball is fired vertically upward off of a cart moving with a constant horizontal velocity, draw it’s trajectory
and say where it will land relative to the cart.
3.
If a ball is fired vertically upward off of a cart that is experiencing a horizontal acceleration, draw it’s trajectory
and say where it land will relative to the cart.
4.
If a ball is fired upward perpendicular [normal] to the plane of a steep inclined plane, draw it’s trajectory and
say where it will land relative to the cart.
5.
The barrel of a tranquilzer gun is aimed at a monkey. The monkey drops from its branch at the same
instant the gun was fired. The monkey is a horizontal distance of 45.0 m from the initial muzzle velocity. Given
the muzzle velocity of the dart was 220.0 m/s 10o above the horizon. Will the monkey get hit ? If so determine
how far above the ground the monkey will be when it gets hit. [ANS 7.73M ABOVE THE GROUND]
6.
How are the sight angles from a gun’s sights related to the actual angle of the gun’s barrel and muzzle
velocity? Include a diagram in your explanation.
7.
Find the resultant of combining 148 m/s N45oW, with 148 m/s E60oN and 148 m/s E75oN.
[ANS =378m/s N1.2oE]
8.
A car traveling at 30.0 m/s on level ground runs off a cliff. It strikes the water below in 4.00s. Determine the
car’s velocity as it hits the water.
9.
[ANS = 49.4 m/s ê37.3oè]
A football is kicked at an angle of 30o to the horizontal with a velocity of 20.0 m/s determine:
a. How long the ball is in the air
[ANS = 2.04s]
b. How far the ball will go
[ANS = 35.3m]
c. The maximum height the ball will reach [ANS = 5.10m]
4
Cannonball
10.
50 m
A cannon ball is fired horizontally at a speed of 150.0 ms-1 -1from the top of a cliff that is
27 ms
50.00 m high.
550
22 m
45 m
3 ms-1
How far from the base of the cliff will the cannon ball land?
[ANS = 478.9m]
11.
A golf ball is hit at an angle of 30o and rises to a maximum height of 40.00 m. What was
the initial velocity of the ball ?
[ ANS = 44.84m/s è 30oé]
12.
In one of Galileo’s famous “thought” experiments he imagined that a cannonball was
dropped for the top of the mast of a moving ship.
Suppose the boat’s forward speed was 3.00 ms-1 and the mast was 22.0 m high, the
position that the cannonball would land would be approximately…(answer relative to the
boat, and relative to the water)
[ANS = 0.00m relative to the boat
12.7m relative to the water]
13.
In training, a baseball batter hits a ball at a speed of 27 ms-1 and an angle of 550 towards a
vertical metal fence that is 45 m away.
How far from the initial height does his ball strike the fence?
[ANS = 23m up]
5
CIRCULAR MOTION & GRAVITAION
Circular Motion
2.0 m
ICE
h m length of string. The stopper is swung
A 0.013 kg rubber stopper is attached to a 0.93
in a horizontal circle, making one revolution in 1.18 s. (T = 1.18 s)
a.
Find the centripetal force exerted by the string.
[ANS = 0.343N centripetal]
b.
Find the stopper’s velocity.
[ANS = 4.95 m/s tangential]
Racing on a flat track, a 1500.0 kg car going 20.0 m/s rounds a curve 56.0 m in radius.
What would be the minimum coefficient of static friction between tires and road that
would be needed for the car to round the curve without skidding? [ANS = 0.73]
How would the coefficient change for a car twice the mass?
[ANS it would be the same]
Calculate the tension force of a 0.900 metre arm on a vertically swinging pail of water in
a circle (like class demo), with a mass of 7.00 kg, velocity of 3.00 m/s:
a.
at the bottom of the circle
[ANS = 139N up]
b.
Why is the tension at the top of the circle less than at the bottom?
1.
2.
3.
[ANS the force of gravity is also acting downward, reducing
the tension needed to equal the net centripetal force.]
4.
A toboggan cannot rely on the frictional force of ice to produce centripetal acceleration
round bends. The bend on an Austrian toboggan run has a radius of 40.0 m. The ice at the
bend has a curved surface of radius 2.00 m. Note this is a circular banked curve problem.
If a 200.0 kg toboggan goes round this bend on the run at a speed of 19.8 ms-1;
a. What centripetal force is required on the toboggan?
[ANS = 1960N]
b. What angle will the toboggan form with the inclined plane as it travels? [ANS = 87 ]
c. Using that angle and simple geometry determine to what vertical height (h) must
the toboggan rise up the ice surface above the ground?
[ANS = 1.89m]
5.
Why is centrifugal force a fictional force? What is the real force and what kind of acceleration can it cause?
o
Explain with the aid of a diagram.
6.
What is geostationary orbit? Do those orbits occur in a variety of heights above the Earth? Explain.
7.
A rubber ball is swung around and around in uniform circular motion with a frequency of 36 rpm and a radius
of 50.0 cm. The mass of the rubber stopper is 250.0 g.
a.
Determine the maximum and minimum tension in the string on the rubber stopper if it is swung in uniform
horizontal motion.
b.
[ ANS = there is not max or min, it stays constant at 1.78N centripetal]
Determine the maximum and minimum tension in the string on the rubber stopper if it is swung in uniform
vertical motion.
[ANS = Ft max= 2.02N ê Ft min= 1.52Nê]
6
cable
8.
30o30
o
What is the speed of a spy satellite in an orbit of 300.0 km above the Earth’s surface?
60o often ‘rove’ above the
Note this is different than a geostationary satellite. Spy
strutsatellites
10.0
kg
surface of the earth.
9.
[ANS
= 7700m/s tangential]
Mass
A race track has a radius of 200.0 m and is designed to allow motorbikes
to travel
supported
around the curve without the aid of friction at speeds of 150.0 km/h. Determine the
angle at which the curve must be banked.
o
[ANS = 41.5 ]
STATIC EQUILIBRIUM
1.
What is a simple technique that can be used to determine the center of mass of any
object? (hint think cardboard exercise…)
2.
A bag of clothespins hung in the middle of a 3.00 m clothesline cause the line to dip 1.5o
below the horizontal at each end.
a. Draw a free body diagram for this situation.
b. What is the mass of the cloths if the tension in the line is 85.0 N?
3.
4.
[ANS = 0.45 kg]
What is torque and how is different from other forces?
What is the torque from the vertical cable on the 2.000 m
rod, of negligible mass, that is supporting a 10.00 kg mass
at an angle of 60o to the wall?
[Let a clockwise torque be "+"]
[ANS = 169.9 Nm]
5.
a.
What maximum mass can be supported by a strut and cable
arrangement similar to the diagram to the right, if the maximum force on
the cable can be 2500.0 N before it rips out of the wall?
b.
[ANS = 127.4kg]
How would the maximum mass supported change if the angle was doubled
to 60o?
[ANS = 220.7kg]
7
2. Given a 2.0 m long rod with a 1.0 kg mass at one end and a 3.0 kg mass at the other end.
Support
Support
1
2
a. Determine the center of mass of the system if the mass of the rod is negligible.
b. What is the tension in the string holding the mobile?
3.0 kg
See diagram.
[ANS = 0.50m]
[ANS = 39.2N up]
1.0 kg
3. Two
children of masses 17 kg and 27 kg sit at opposite ends of a 3.8 m teeter-tooter that
is pivoted at the center. Where should a third child of mass 20.0 kg sit in order to
balance the ride? Does the mass of the teeter-totter plank matter?
4. The
[ANS = 0.95m]
hand, forearm, and upper arm of a gymnast have masses of 0.400 kg 1.20 kg, and
1.90 kg respectfully, and their respective centers of mass are 0.600 m, 0.400 m , and
0.150m from her shoulder joint. Find the center of mass of her unbent arm as it is held
horizontally from her shoulder.
5. A
[ANS = 30.0cm from the shoulder]
square table is 0.600 m long with a center of mass 0.600 m above the ground. What is
the tipping angle?
o
[ANS = 26.6 ]
10. A 4.000 m, 30.00 kg uniform diving board (its center of mass is 2.000 m from both ends)
rests on two supports. The diving board pivots on support 1 and is supported freely by
support 2. Determine the magnitude of the force on support 2 when a 25.00 kg child
stands at the end of the diving board. Support 2 is 1.200 m from the Center of the
diving board.
[ANS = 1962N up]
8
Electric Circuits.
1. A 20.0-m length of a wire 1.80 mm in diameter has a resistance of 2.50 Ω. What is the
resistance of a 35.0-m length of wire 3.00 mm in diameter made of the same material?
[ANS = 1.59 Ohms]
2.
Suppose you want to install a heating coil that will convert electric energy to heat at a
rate of 300 W for a current of 1.5 A. The resistivity of the coil wire is 1 x 10-6 Ω/m, and
its diameter is 0.3 mm. Determine its length.
3.
What is the internal resistance of a 12-V car battery whose terminal voltage drops to 7.5
V when the starter draws 80 A?
4.
[ANS = 9.40m]
[ANS = 0.094 Ohms]
A battery with an emf of 12 V and internal resistance of 0.9 Ω is connected across a
load resistor R. If the current in the circuit is 1.4 A, what is the value of R? [ANS
5.
7.7 Ohms]
A three-way light bulb can produce 50 W, 100 W or 150 W at 120 V. Such a bulb
contains two filaments that can be connected to the 120 V either individually or in
parallel. Describe how the connections to the two filaments are made to give each of
the three powers. What must be the resistance of each filament?
6.
How many 100-W light bulbs, operated at 120 V, can be used in a single parallel circuit
without blowing a 15-A fuse?
7.
[ANS= 144 & 288 ohms]
[ANS = 18 light bulbs max]
If all you have is a 120-V line, would it be possible to light several 6-V lamps without
burning them out. How could this be done?
8.
Two light bulbs of resistance R1 and R2 (R1 > R2) are connected in series. Which is
brighter? What if they are in parallel?
9
9.
Find the voltage and current experienced through each resistor along with the total
resistance of the circuit.
Given
Vs= 12 v
R1=9.0Ω
R2=6.0Ω
R3=18.0Ω
RM= 3.0Ω
[ans Rt= 29.0 ohms; Vm=7.4v, Im=0.41A ….]
10.
Find the voltage and current experienced
through each resistor along with the total
resistance of the circuit.
Note {k Ohm =kΩ=1000Ω }
[ANS = Rt=873 ohms; V1=3.28v …]
11.
Given the electromagnetic force (emf) driving the circuit is 9.00v and all of the resistor
are16.0Ω, determine the voltage and current experienced through each resistor along
with the total POWER USED (using the total voltage & total current)
{ANS = Rt=24.0 ohms; I2=0.19A ….]
10
Electromagnetic Induction
12.
An electron traveling horizontally enters a region where a uniform magnetic field is directed into the plane of the paper as shown.
Which one of the following phrases most accurately describes the motion of the electron once it has entered the field?
13
An electron enters a region that contains a magnetic field directed into the page as shown. The velocity vector of the electron
makes an angle of 30° with the +y axis. What is the direction of the magnetic force on the electron when it enters the field?
14
A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown
in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam
travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 × 10–27 kg and e
= 1.6 × 10–19 C. Which ion falls at position 2?
11
15
16
A long straight vertical segment of wire traverses a magnetic field of magnitude 2.0 T in the direction shown in the diagram. The
length of the wire that lies in the magnetic field is 0.060 m. When the switch is closed, a current of 4.0 A flows through the wire
from point P to point Q.
Which one of the following statements concerning the effect of the magnetic force on the wire is true?
A. The wire will be pushed to the left.
B. The wire will be pushed to the right.
C. The wire will have no net force acting on it.
D. The wire will be pushed downward, into the plane of the paper.
E. The wire will be pushed upward, out of the plane of the paper.
17
18. Which one of the following statements concerning the magnetic field well inside a long, current-carrying solenoid is true? Explain why
they are true, or why they are false.
A. The magnetic field is zero.
B. The magnetic field is non-zero and nearly uniform.
C. The magnetic field is independent of the number of windings.
D. The magnetic field is independent of the current in the solenoid.
E. The magnetic field varies as 1/r as measured from the solenoid axis.
12
19. Two loops carry equal currents I in the same direction. They are held in the positions shown in the figure and project above and
below the plane of the paper. The point P lies exactly halfway between them on the line that joins their centers. The centers of the
loops and the point P lie in the plane of the paper. Which one of the figures below shows the position of a compass needle if the
compass were placed in the plane of the paper at P?
20.
21.
How does a generator work? Explain in full with well-labeled diagrams.
Your answer should take 1-2 pages.
21.
How does a transformer work? Explain in full with well-labeled diagrams.
Your answer should take 1-2 pages.
WORK AND ENERGY
1.
What is work? And how is it similar and different from energy? Compare and contrast the
physics definition with the common understanding of ‘work’.
2.
What are the main types of energy?
3.
What is the law of conservation of energy? If energy is conserved why do freely swinging
pendulums always slow down and stop having no mechanical kinetic or potential
energy?
4.
A football is kicked at an angle of 30o to the horizontal with a velocity of 20.0 m/s
determine its maximum height using only energy concepts. How does this compare to
doing it the kinematic way?
[ANS = both ways give h=5.10m]
13
6.0 m
5.
A 1300 kg car traveling at 30.0 m/s on level ground runs off a cliff falling 78.4 m.
Determine the car’s speed as it hits the water. Why can’t we find the car’s velocity if we
Bank
use energy concepts?
6.
Given the 1300 kg car fell for 4.0 s determine the power exerted on the car by gravity
throughout the fall.
7.
[ANS = 49 m/s]
[ANS 250 kiloWatts]
2.0 m
How can work be determined from a force versus distance graph? Explain with graph
example.
8.
An astronaut on a strange planet finds that she can jump a maximum horizontal
distance of 30 m if her initial speed is 9 m/s, and she leaves the ground at 45 o .
What is the value of g on this planet?
9.
[ANS = 0.675m/s/s]
Harry decides to swing on a rope attached to a tree branch and into the river.
The rope is 6.0 m long and hangs vertically down so its end is 2.0 m above the water.
Harry climbs up the bank, hold the rope tightly at its end, swings down in a vertical circular
arc and lets go exactly at the bottom of its swing.
How far from the bank does Harry land in the river? Ignore air resistance.
[ANS = 12.93m]
10.
A bullet of mass 5.0000 g has a speed of 500.00 m/s. It penetrates a 4.0000 cm thick
piece of wood and emerges with a speed of 200.00 m/s.
a) What is the change in the kinetic energy of the bullet ?
[ANS = -525J]
b) What average force did the wood exert on the bullet ?
[ANS = 13125 N]
14
11.
A second 5.00 g bullet is shot horizontally, and becomes embedded in a 5.0000-kg
block of wood. The block is suspended by a long cord. After impact, the block is seen to
swing in a circular arc, rising to a height of 75.0000 cm above its original level. What
was the initial speed of the bullet ?
12.
[ANS = 3840m/s]
A 25-kg mass, initially at rest, slides down an incline 4.0 m along its slope and 15 m
high. At the bottom, the speed of the mass is 14 m/s.
a) Explain how one may determine whether the incline is frictionless or not.
13.
b) What is the magnitude of the frictional force ?
[ANS = 3.06N]
c) How much work was done by the force of friction ?
[ANS = 120J]
Two objects collide in a head on collision. The first object has a mass of 2.50 kg and
an initial velocity of 4.00 m/s East, the second object has a mass of 5.00 kg and has an
initial velocity of 3.00 m/s West. Given the two balls collide elastically, determine the
final speed of both balls after the collision.
14.
[ANS V1f=5.2 m/s left; V2f=1.7m/s right]
How would the situation described in #20 be different if the second ball was initially at
rest? What would the final speed of each of the balls be?
15.
[ANS V1f=1.3 m/s W; V2f=2.7m/s E]
Using the laws of the conservation of momentum and the conservation of energy derive
the expression
V1i + V1 f = V2i + V2 f
16. A 1250 kg car slows down from 90.0 km/h to 70.0 km/h in about 5.00 seconds on a
horizontal road when in neutral. Approximately what power (in watts & horse power)
is needed to keep the car traveling at a constant speed of 80.0 km/h?
[Note: 1 hp = 746 W]
[ANS = 41.7 hp]
15
70
60
50
FORCE (N)
40
Impulse
((N)
30
1.
and Momentum
20
The
graph below shows a force/ time plot for a golf ball being struck by a club.
10
0
1
2
5
3
4
TIME (mS)
(ms)(m(MILLISECOND
S)
6
7
8
From the graph, determine the impulse given to the club over the first 7 milliseconds.
[ANS = 0.210J]
2.
A ball of mass 0.150 kg is thrown toward a batter at a speed of 20.0 m/s. The batter
drives the ball straight back toward the pitcher with a speed of 30.0 m/s.
a) What impulse acts on the ball during collision ?
[ANS = 7.4 Ns]
b) If the pitcher catches the ball in a collision which lasts only 0.030 s, what is the size of
the average force does the pitcher experience ?
3.
[ANS = 250 N]
A 5.00 kg body at rest is torn apart by an explosion. A 3.00 kg piece is seen to move to
the right at a speed of 50.0 m/s. Determine the motion of the remaining piece.
[ANS = 75 m/s left]
4.
What can be done to catch an egg thrown from a considerable distance, without
breaking it? Explain why this maneuver works using the ideas discussed in this unit.
5.
Why does an untied inflated balloon fly around the room when it is released from rest
while lying horizontally? Include a diagram in your explanation.
6.
A 1250 kg mid sized vehicle traveling at 100.0 km/h northbound hits the brake as a
precautionary measure to avoid hitting some deer that were crossing the road. The
vehicle slows to a speed of 20.0 km/h, over at time of 2.5 s. Calculate the average
force acting on the truck.
[ANS = 11100 N south]
16
7.
Consider a cross check situation between two hockey players: one a 90.0 kg Montreal
Canadian traveling at 28.8 km/h west who cross checks the other, a 105 kg Toronto
Maple Leaf player traveling at 10.8 km/h west, from behind. Given the Montreal
Canadian player travels at 14.4 km/h west after the check, Calculate the final velocity
just after the check of the Toronto Maple Leaf’s player.
[ANS = 6.4m/s W]
8.
A soccer ball of mass 0.500 kg is kicked with a
horizontal speed of 20.0 m/s. If a 65.5 kg
goalie jumps up and catches the ball in mid-air,
what is the horizontal speed (toward the net)
just after the catch?
[ANS = 0.15 m/s backwards]
9.
A hockey player with a mass of 95.0 kg and a momentum of 275 kgm/s [W] collides with
another hockey player with a mass of 100.0 kg and a momentum of 450.0 kgm/s [N30oW].
The hockey players grab onto each other’s jerseys when they collide. Omit all friction
between the skates and the ice. Determine their final velocity just after their collision.
[ANS = 1.1 m/s N49oW ]
17
Metric System
Tm terameter
Gm - gigameter
Mm - megameter
km – kilometer
hm – hectometer
Gravitational
constant:
dam – decameter
meter, gram, liter
dm – decimeter
cm – centimeter
mm - millimeter
Elementary
Charge:
µm - micrometer
nm - of proton:
nanometer
Mass
pm – picometer
fm - of electron:
femtometer
Mass
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1 ml = 1 cm
Coulomb’s constant:
m
m
m CONSTANTS
m
N ⋅ m2
m G = 6.673 × 10 −11
kg 2
m
m
m
m g = 9.81 2 (at the surface of the earth)
s
m
m e = 1602
.
× 10−19 C
m
m m = 167
. × 10 −27 kg
m p
mm = 9.11 × 10 −31 kg
12
9
6
3
2
1
0
-1
-2
-3
-6
-9
-12
-15
e
N ⋅ m2
k = 9.0 × 10
C2
3
9
Magnetic permeability constant of air : µ = 4π x 10 T⋅m/A
-7
air
N
A2
k = 2.0 × 10 −7
Ampère’s constant:
Planetary Data
Name
Sun
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Average radius (m)
Mass (kg)
6.960 x 10
2.43 x 10
6.073 x 10
6.3713 x 10
3.38 x 10
6.98 x 10
5.82 x 10
2.35 x 10
2.27 x 10
1.991 x 10
3.2 x 10
4.88 x 10
5.979 x 10
6.42 x 10
1.901 x 10
5.68 x 10
8.68 x 10
1.03 x 10
8
6
30
23
6
10
24
6
6
11
24
23
7
7
26
7
25
7
26
Mean distance from
sun (m)
---------------5.80 x 10
1.081 x 10
1.4957 x 10
2.278 x 10
7.781 x 10
1.427 x 10
2.870 x 10
4.500 x 10
11
11
27
11
12
12
12
Quadratic Equation
− b ± b 2 − 4ac
x=
2a
Cosine Law
a =b +c – 2bc(cosA)
2
2
2
Sine Law
sin A sin B sin C
=
=
a
b
c
18
FORMULAE & DATA
2
3
mm
Fg = G 1 2 2
r
Fg
g=
m
⎛ Ta ⎞ ⎛ ra ⎞
⎜ ⎟ = ⎜ ⎟
⎝ Tb ⎠ ⎝ rb ⎠
mv 2
F=
r
c = 2 ⋅π ⋅ r
ac = 4 ⋅ π 2 ⋅ r ⋅ f 2
g =G
m
d2
qq
Fe = k 1 2 2
r
q
E=k 2
r
Fe = Eq
W = qV
⎛ 4π2
Tp 2 = ⎜
⎝ GM s
⎞ 3
⎟ r
⎠
EMF = BLv
EMF = N
Vs
Ns
=
Vp N p
Np
Is
=
Ip
Ns
ΔΦ
Δt
V = Ed
Veff = 0.707Vmax
V = IR
B=
T =
kI
r
1
f
F Δt = mΔv
W = Fd cos θ
W = ΔKE
ΣE i = ΣE f
W = ΔPE
ΣPi = ΣPf
KE = 1 m ⋅ v 2
2
PE = mgh
1
d = v f t − at 2
2
Δd
v=
Δt
1 2
at
2
Δv
a=
Δt
d = vi t +
W
P=
t
V2
P=
R
P = I 2R
P = VI
v=
E
B
2qVa
m
v=
Bqr
v=
m
B 2 qr 2
m=
2Va
Fb = qvB = qvB sin θ
F=
kI 1 I 2 L
r
Fb = BIL = BIL sin θ
B=
µ I µ NI µ NI
=
=
2π r
2r
L
q = Ne
Φ = BA
B=
kI
r
1
2
m ( Δv ) + mg Δh
2
W = Δheat
P = m⋅v
Fd =
v f 2 = vi 2 + 2ad
vav =
1
(vi + v f
2
)
v f = vi + at
Fnet = ma
F f = µFN
µ s = tan θ
τ = F ⋅ r ⋅ sin θ
Στ = τ 1 + τ 2 + τ 3 + ...
ΣF = F1 + F2 + F3 + ...
19