Physics 20 – Course Review
*This course review package is intended for review only and not for instruction of the Physics 20 Course
Physics Math related skills:
1. Unit Conversion: mks units using the factor label method 2. Scientific Notation: 1.23 x 104
3. Significant Digits:
a. adding and subtracting: answer has the same number of decimal places as the number with the least.
ex: 3.1 + 3.42 = 6.52 = 6.5
b. multiplying and dividing: answer applies the least number of significant digits from the data used.
ex: 3.1 x 3.42 = 10.602 = 11
4. Formula Manipulation: isolating for different variables of a physics equation Ex:
v d
t t d
solve for " t" v
Problems:
1. If x = g/t then t =?, If x = abc /d then b = ? 2. Put one million and 0.00017 in scientific notation.
3. Solve for the following:
a a. 4.0 x 104 + 3 x 103 b.6.8 x 109 – 5 x 108 c. 3 x 108 / 1.2 x 10-7 b d. (4.7 x 1012)(8.678 x 106)
4. Using unit analysis to show that a = v2/r is a reasonable formula.
5. 0.12 g = kg? 1.35 cm = m?
6. Use correct significant digits:
a. 3.02 kg + 0.04 kg = b. 3.02 N x 0.04 m =
c c. 4 people each ate 432 g of ice cream. What is the total mass of ice cream eaten?
7. Find the sine of angle B and the cosine of angle A.
Kinematics
Kinematics is a study of how objects move. We begin to quantify motion as scalar or vector.
Scalar: Magnitude only. Ex: distance, time, speed
Vector: Magnitude and direction. Ex: displacement, velocity, acceleration, force etc.
Uniform Motion: motion where the velocity is constant. (0 acceleration)
v d
ave t
Graphically: slope of the d vs. t graph yields velocity, area under the v vs. t graph yields displacement
Problems:
8. Sketch a displacement – time graph of the following data using correct graphing guidelines.
9. Find the slope and instantaneous velocity at t = 0.75 s.
d (m)
t (s)
Displacement / time graph
t (s) v
(m/s)
Velocity / time graph
A=bh
Time (s)
Disp.
(m)
0 0
0.10 0.012 0.20 0.024 0.30 0.035 0.40 0.047 0.50 0.060 0.60 0.072 0.70 0.085 0.80 0.097 0.90 0.108 1.00 0.120
b
c
3 5
4 a
10. What type of motion is displayed by the graph?
11. A car travels from Edmonton to Calgary (300 km). If it takes 3 h and 20 min. to make the trip, what is the average speed of the car?
12. A train travels 68 km/h for 1.5 h North and 56 km/h for 2.0 h South. What is the train’s average speed? What is the train’s average velocity?
Uniform Accelerated Motion:
Motion where an object changes velocity uniformly over time.
Graphically:
The Instantaneous velocity may be found by using the slope of a line tangent to the curve of the d vs. t graph. Acceleration may be found by using the slope of the v vs. t graph. Displacement may be found solving for the area under the v vs. t graph.
Mathematically:
t v a vf i
d vit12at2 vf2 vi2 2ad v v t
d f i
2
Problems:
13. A car reaches 100 km/h in 14 s starting from rest. The average acceleration is?
14. A ball rolls down a 90 cm long incline in 3.0 s. What was its acceleration?
15. A car travelling at 36 km/h accelerates at 2.5 m/s2 for 6.0 seconds. Find the final speed and the distance traveled while accelerating.
Free-fall:
objects being released and falling linearly due to the acceleration of earth’s gravity. - 9.81 m/s2 Problems:
16. A coconut falls from a tree and reaches an impact velocity of 85 km/h. For how long did it fall?
17. An object is thrown upwards with a velocity of 14.7 m/s. How long will it continue to rise?
18. A student drops a grape and a bowling ball. The grape hits the ground 4 s later. How far did it fall? How long would it take the bowling ball to hit the ground and how fast is it moving upon impact (ignoring air resistance)?
19. A stone is dropped from a balloon descending at 20 m/s when the balloon is 700 m above the ground. How long does it take the stone to hit the ground?
Vectors:
Definition: A quantity of motion that has magnitude and direction
Resolving displacements, velocities or forces in terms of their magnitudes and directions.
Skills: Resolving x & y components, adding components to find the resultant vector, using trigonometry to find the resultant direction and describe the direction using polar or rectangular coordinates (RCS).
a (m/s2)
t (s)
Acceleration / time graph
d (m)
t (s)
Displacement / time graph
t (s) v
(m/s)
Velocity / time graph
A=1/2 bh
E of N
N of E S of E
E of S W of S
S of W W of N
N of W 180
270
90
0
vy = v sin
vx = v cos v
sin .
opp.
hyp cos .
adj.
hyp tan .
opp.
adj a2 b2 c2
Problems:
20. Consider the vector 10 m/s 135. Find the x and y components.
21. A dog walks 4.0 m E, 5.0 m N, 6.0 m W, 7.0 m S, and 4.0 m E. What is the dog’s displacement?
22. A canoeist who can paddle 3.0 m/s heads straight across a 400 m wide river. If the water flows 1.4 m/s, how far down river will he land? And what is the velocity of the canoeist with respect to the shore?
23. Find the resultant velocity of a plane travelling west at 300 km/h being acted upon by a north wind blowing 80 km/h.
Projectile Motion:
Motion with two components to it (Uniform Motion in the x-direction and uniform accelerated motion in the y-direction) where time is independent of both.
a. The Horizontal projectile: b. Projectile at an angle
Problems:
24. An object is thrown from a cliff with a horizontal velocity of 20.0 m/s. It takes 4.20 s to reach the ground. How far from the base of the cliff did it land?
25. An object is thrown horizontally from an 85.0 m building. It lands 67.8 m from the base of the building. What was it’s velocity just before it hit the ground?
26. A ball is thrown at a 30.0 angle and reaches a maximum height of 5.75 m. With what velocity was it thrown?
27. The same ball is kicked at a velocity of 25.0 m/s. If it travels a range of 25.0 m and was in the air for 2.15 s, at what angle was it thrown?
Dynamics:
A study of how objects move Newton’s Three Law’s:
1. Law of inertia: Objects remain at rest or at a constant velocity unless acted upon by an unbalanced force
2. F=ma: acceleration of an object varies directly with the force and inversely with the mass.
3. “Action Re-action” Law: For every action there is an equal and opposite reaction.
Forces in nature:
Weight (Fg =mg)
d=
v
t=
dh = y-dir vh = x-dir
a= 9.81 m/s2
t=
vv= vf=
dh = vf = -v
v
v
t=
dh = y-dir vh= x-dir
a= -9.81 m/s2
t=
vv =
vf = -vi
vf = 0
Normal Force (FN):
a. horizontal surface: FN = Fg
b. on an incline: FN = Fg cos
Force of friction: Ff = FN
Applied force (FA) Free-body diagrams:
FNet = F1 + F2 + F3 + . . . ma = F1 + F2 + F3 + . . .
Problems:
28. What average force is required to stop a 1000kg car in 6.0 s if it is travelling at 90 km/h? How far does the car travel?
29. What is the acceleration of a falling 65 kg skydiver if air resistance exerts a force of 250 N?
30. A rocket has a mass of 1.00 x 105 kg. Its engines develop a thrust of 2.50 x 106 N, what is the acceleration of the rocket?
31. A car is travelling on a level highway at a speed of 15 m/s. A breaking force of 3,000 N brings the car to a stop in 10 s. What is the mass of the car?
32. Find the force needed to accelerate a 50 kg crate up a 30.0 incline at a rate of 1.2 m/s2. 33. A 1200 kg elevator is lowered at a constant velocity. Find the tension in the cable.
34. Two 4.0 kg masses are pulled by 2.5 kg mass on a horizontal air track. What is the acceleration of the system? Find the tension between the two 4.0 kg masses.
35. Two forces pull a 7.00 kg object: 20.5 N East and 32.0 N 67.5 South of East. Find the force needed to keep the object stationary.
Ff
FN
Fii= Fg sin Fg
Fg Ff
FN
FA
Fh= FA cos
FA
a a
Fg
Down:
FNet = F
1 + F
2. . ma = F
g + (-F
A)
up:
FNet = F
1 + F
2. . ma = F
A + (-F
g)
m1
Fg m2
FA Ff
a
a FNet = F1 + F2 + . .
mtotala = Fg + (-Ff) a =
FA = m
pulleda
Fg m3
m2 Ff
a
a m1
FNet = F1 + F2 + . . mtotala = F
g + (-F
f) a =
FA = mpulleda FA
FA
Force to keep equilibrium
F1
F2
Circular Motion, Universal Gravitation, and Periodic Motion
T v 2r
r
ac v
2 F mv
r
rm
c T
2 2
2
4
Fc Fg v rg
Kepler’s Laws:
1. Law of ellipses 2. Law of Equal areas 3. Law of periods
Newton’s Universal Law of gravitation: The gravitational force of attraction between any two objects with mass
F Gm m
g d12 2 units (N)
Satellites: Fc = Fg
Gravitational Field Theory: Any object with mass produces a field of attraction toward it’s center Inverse Square Law: F
g d12 R2
Gm m
ag Fg p units: N/kg = m/s2
Problems:
36. A car (2000 kg) is traveling at 40 m/s around a 400 m diameter racetrack. What is the car’s acceleration (magnitude and direction) when it is on the east side of the track?
37. What is the force acting on the car above?
38. A bowling ball exerts an attractive force on the pins. If the mass of the bowling ball is 5.0 kg and each pin has a mass of 1.0 kg. What is the force of attraction when they are 20.0 m apart?
39. What is the magnitude of the force before they hit (assume 1.0 mm distance between the two).
40. What is the velocity of a satellite orbiting the earth at a radius of 1500 km above the surface?
41. What is the period of the above satellite?
42. If the satellite has a mass of 350 kg, what is the force acting on it?
43. If you travel to a planet that has twice the mass of earth and half the radius, what would happen to your weight?
P1
P2
1.
A1 A2
A1 = A
2. 2 3. T
R
T R
12 1
3
22 2
3 v
ac Fc
F
d
F
1/d2
Curve straightening
Object with mass
Work:
) (EK E mgh Fd
W is a scalar quantity measured in joules (J).
Power: Is the rate of doing work measured in watts (W) t Fv mgh t
mad t
Fd t
P W
Energy: EP mgh EK 12mv2
Problems:
44. 50 J of work is done on a football kicked at an angle of 30.0 from the horizontal a. If the football has a mass of 1.2 kg, find the maximum speed
b. What is the maximum height the football reaches?
c. What is the distance the football travels?
45. An object has a mass (m) and a velocity (v) and a kinetic energy of 0.5 J. If it’s mass and velocity is doubled, what is its new kinetic energy?
46. An object is dropped from a height of 25 m. What is its velocity just before it hits the ground?
Periodic Motion:
Motion that repeats itself over the same path.
Pendulums:
f g T 2 l 1
Curve straightening
Problems:
47. A pendulum bob is displaced from equilibrium by 1.8 m vertically. How fast will it be moving when it swings past the rest position?
48. If the length of a pendulum is doubled, what happens to the period?
49. What is the energy in a pendulum that has a mass of 0.050 kg and a velocity of 1.2 m/s as it passes through the equilibrium point?
50. What is the direction of acceleration for a pendulum displaced from equilibrium?
T (s)
L (m) L (m)
T2
ET = E
p = mgh
ET = Ep + EK ET = Ep = mgh
ET = E
K = ½ mv2
Simple Harmonic Motion:
Hooke’s Law: F = -kx (restoring force) – k (N/m)
Fx
W Ep 12kA2 Ek 12mvo2
2 12 2
12kx mv
E E
ET p K
Law of Conservation of Mechanical Energy in a Spring:
Simple Harmonic Oscillation:
f k
T m 1
2
Problems:
51. What is the spring constant of a strip of wood that, following Hooke’s Law, is compressed 0.10 cm by a force of 180 N?
52. The shock absorbers in a 1000 kg car follow Hooke’s Law. If the mass of the car causes an average compression of 0.015 m, what is the spring constant of each of the four absorbers?
53. A mass vibrates along a frictionless horizontal surface. The spring constant is 18 N/m. What is the mass’s displacement if it’s potential energy is 4.5 J?
54. The same mass has a maximum velocity of 0.35 m/s and a maximum displacement of 0.29 m, what is the velocity of the mass when the displacement is: 0.29m, and 0.10m?
Frictionless
F=-kx
Max.
displacement ET = E
P = ½ kA2
Eq.
ET = E
K = ½ mv2 Passing through the Eq. pojnt (max.
velocity) Between
max A and Eq.
ET = E
P + E
K
F=-kx
ET = EP = ½ kA2 F=-kx
Max.
displacement (compression)
Mechanical Waves
Transverse Wave Longitudinal Wave
Universal Wave equation: vf
Law of Reflection: of incidence = of reflection Law of Refraction: sin
sin
i r
i r
i r
v v n
Diffraction: the spreading out of waves through a barrier Interference, constructive, destructive
Doppler Effect: f f V v V v
o
a o
a s
'
Frequency (f) = pitch
Beat frequency: # of beats f1 f2 Standing waves:
Air Columns:
Problems:
55. A 10 Hz wave has a 2 cm wavelength. What is the velocity?
56. Waves passing through a barrier diffract. What are two ways of increasing diffraction?
57. A tuning fork has a frequency of 1000 Hz. It emits sound waves of speed 340 m/s. How many waves are produced in 0.10 s?
58. A 512 Hz tuning fork is held over a variable length closed tube. When resonance is first heard the tube is 17 cm long. What is the speed of sound?
59. Completely destructive interference of sound waves sounds like what?
60. Two sound sources, which have very similar frequencies, cause what?
61. A truck siren (1.20 kHz) has an apparent pitch of 1.10 kHz to a stationary observer when the speed of sound is 348 m/s due to the temperature and humidity outside, what is the velocity of the truck?
crest crest
A
trough
Compression Rarefaction
node
anti-node
Closed: L= /4
L
Harmonics:
1,3,5,7,9, . . .
Open: L= /2
L
Harmonics:
1,2,3,4,5, . . . vo + travels toward the source
- travels away from source vs + travels away from observer - travels towards the observer
O = observer S = source
