Welcome to AP Physics! Mr. Clark will be holding a Math Summer Bridge Camp this summer to help students learn some math to help lessen the beat down you will experience in the course. Mr. Clark and I highly recommend you attend this 2 hour session during the June intersession. The class will pay dividends in the long run.
1. The AP exams are in early May which requires a very intense pace. We will start on the physics subject matter the very first day of school. This assignment will help with valuable skills which you will use throughout the AP course.
2. AP Physics requires a proficiency in algebra, trigonometry, and geometry. AP physics is a course in applied mathematics. The assignment includes mathematical problems which are considered routine in AP Physics. This includes key metric system conversion factors and how to use them, understanding vectors, and graphing.
3. I have an Edmodo AP Physics 1 group where course materials are available on Edmodo.com The course code to join the AP Physics I group is 46agb6.
The math review is to be completed with all work shown. No miracles!!
a. The following are ordinary physics problems. Place the answer in scientific notation when appropriate; for example, 200 is easier to write than 2.00 x 102, but 2.00 x 108 is easier to write than 200,000,000. Do your best to cancel units and show the simplified units in the final answer. Do the math and record the answer here.
a. Ts=2∙π∙0.045 kg2000 kgs2 =
b. K=0.5∙660 kg∙ 2.11 x 104 ms2 =
c. F= 9x 109 N∙m2C2 ∙ 3.2 x10-9 C ∙ 9.6 x 10-9 C0.32 m2 =
d. 1Rp= 1450 Ω+ 1940 Ω =
e. e= 1700 J-330 J1700 J =
f. 1.33∙sin25=1.50∙sinθ ; find θ
g. Kmax= 6.63 x 10-34 J∙s ∙7.09 x 1014 s-2.17 x 10-19 J
h. γ= 11-2.25 x 108 ms 3 x 108 ms
b. Problems on the AP exam are often done with variables only. Solve for the variable indicated. Don’t let the different letters confuse you. Manipulate the equations algebraically as if the variables were numbers. This one will have to be done on a separate sheet of paper.
a. v2= vo2+2∙a∙s- so for a:
b. K=12∙k∙x2 for x:
c. Tp=2∙π∙lg for g:
d. Fg= G∙m1∙m2r2 for r:
e. m∙g∙h= 12∙m∙v2 for v:
f. x= xo+ vo∙t+12∙a∙t2 for t:
g. B= μo∙I2∙π∙r for r:
h. xm= m∙λ∙Ld for d:
i. P∙V=n∙R∙T for T:
j. sinθc= n1n2 for θc
k. q∙V= 12∙m∙v2 for v:
l. 1f= 1do+ 1di for di
c. Science uses the KMS or SI units of measure. KMS stands for kilogram, meter, second. The equations in physics depend on unit agreement, so you must convert to KMS in most problems to arrive at the correct answer. Other conversions will be presented as needed. Examples of common conversions:
a. Kilometers (km) to meters (m) and meters to kilometers
b. Centimeters (cm) to meters (m) and meters to centimeters
c. Millimeters (mm) to meters (m) and meters to millimeters
d. Micrometers (μm) to meters (m) and meters to micrometers
e. Nanometers (nm) to meters (m) and meters to nanometers
f. Gram (g) to kilogram (kg)
g. Celsius (°C) to Kelvin (K)
h. Atmosphere (atm) to Pascals (Pa)
i. Liters (L) to cubic meters (m3)
If you don’t know the conversion factors, they are available online. Colleges and employers need students to be able to find their own information – so here is some practice! This one will have to be done on a separate sheet of paper.
a. 4008 g to kg
b. 1.2 km to m
c. 823 nm to m
d. 298 K to °C
e. 0.77 m to cm
f. 8.8 x 10-8 m to mm
g. 1.2 atm to Pa
h. 25 μm to m
i. 2.65 mm to m
j. 8.23 m to km
k. 5.4 L to m3
l. 40.0 cm to m
m. 6.23 x 10-7 m to nm
n. 1.5 x 1011 m to km
d. Solve the geometry problems. You can do these on this page.
a. Line B touches the circle at a single point. Line A extends through the center of the circle.i. What is line B called in reference to the circle?
ii. How large is the angle between lines A and B? /
b. What is angle C? /
c. How large is angle θ? /
d. The radius of a circle is 5.5 cm.
i. What is the circumference in meters?
ii. What is its area in m2?
e. What is the area under the curve at the right? /Calculate the area of the following shapes. It may be necessary to break up the figure into common shapes.
Calculate the unknown angle values for questions 3-6
Right Triangles & Trigonometry
Suppose you wanted to get from point A to point C in the following diagram. You could go directly from A to C, or you could go to the right from A to B and then go straight up from B to C. Thus the direction we go is important. We will define the distance from C to A as our displacement. You’ll see shortly that the displacement is a vector. In many cases, we will be interested in the x and y component of a vector. In this case, the x component is AB. The y component is BC. /Pythagorean Theorem
If two of the three sides of a right triangle are known, we can find the 3rd side using the Pythagorean Theorem.Recall that a2 + b2 = c2
122 + 52 = c2
144 + 25 = c2
169 = c2
13 = c /
Right Triangle Trigonometry
Both of the triangles shown are right triangles. Angle α is the same for both. Side c is the hypotenuse. Side a is adjacent to angle α. Side b is opposite angle a. If we divided side b by side a for both triangles we would get the same number. The only way we could get a different ratio would be if the angle changed. For example, if the angle increased, side b would have to increase, while side a remained the same. That would cause the ratio to increase. We call the ratio of side b to side a the tangent of the angle. The same logic is true for the ratios of any two sides. We will use three ratios:An easy way to remember these is the acronym SOH CAH TOA (pronounced so-ca-toe-a):
SOH → Sine is Opposite / Hypotenuse
CAH → Cosine is Adjacent / Hypotenuse
TOA → Tangent is Opposite / Adjacent
Make sure the calculator is in the degree mode.
Example: find sides b and c.tanα= oppositeadjacent= ba
tan25= b10
b=10∙tan25=4.66 /
Now that you know side b, you can use trig or the Pythagorean theorem to find side c.
Finding anglesSince each angle has a unique sine, cosine and tangent value, we can use these values to find the angle. We call these functions the inverse tangent, inverse sine, or inverse cosine.
α=tan-1 oppositeadjacent= tan-1 ba
This is read as: α is the angle whose tangent is b/a. /
Example: α=tan-1 oppositeadjacent= tan-1 512=22.62°; the inverse functions are normally above the standard trig function on the calculator and you have to use the shift key or 2nd key.
For the right triangle to the right, determine:
a. the length of side a?b. the sine of angle α?
c. the cosine of angle a?
d. angle α = ______degrees.
e. angle β = ______degrees.
(use trig and check to see if all the angles add to 180o) /
Calculate the following unknowns using trigonometry. Use a calculator, but show all of your work. Please include appropriate units with all answers. (Watch the unit prefixes!)
You will need to be familiar with trigonometric values for a few common angles. Memorizing this unit circle diagram in degrees or the chart below will be very beneficial for next year in both physics and pre-calculus. How the diagram works is the cosine of the angle is the x-coordinate and the sine of the angle is the y-coordinate for the ordered pair. Write the ordered pair (in fraction form) for each of the angles shown in the table below
Refer to your completed chart to answer the following questions.
10. At what angle is sine at a maximum?a. At what angle is sine at a minimum?
b. At what angle is cosine at a minimum?
c. At what angle is cosine at a maximum?
d. At what angle are the sine and cosine equivalent?
e. As the angle increases in the first quadrant, what happens to the cosine of the angle?
f. As the angle increases in the first quadrant, what happens to the sine of the angle?
Use the figure to the right to answer the next two questions.a. Develop an equation for h in terms of l and θ.
b. What is the value of h if l = 6 m and θ = 40°. /
Vectors
Two videos which may help you with working with vectors.
http://www.khanacademy.org/science/physics/v/introduction-to-vectors-and-scalars
http://www.khanacademy.org/science/physics/v/visualizing-vectors-in-2-dimensions
Most of the quantities in physics are vectors. This makes proficiency in vectors extremely important.
Magnitude: Size or extent. The numerical value only.
Direction: Alignment or orientation of any position with respect to any other position.
Scalars: A physical quantity described by a single number and units. A quantity described by magnitude only; a number and unit only. Examples: time, mass, and temperature.
Vector: A physical quantity with both a magnitude and a direction. A directional quantity. Examples: velocity, acceleration, force.
Notation: A or A
Length of the arrow is proportional to the vectors magnitude. Direction the arrow points is the direction of the vector.
Negative Vectors
Negative vectors have the same magnitude as their positive counterpart. They are just pointing in the opposite direction.
– A
Vector Addition and subtraction
Think of it as vector addition only. The result of adding vectors is called the resultant R.
So if A has a magnitude of 3 and B has a magnitude of 2, then R has a magnitude of 3 + 2 = 5.
When you need to subtract one vector from another think of the one being subtracted as being a negative vector. Then add them.
A negative vector has the same length as its positive counterpart, but its direction is reversed. So if A has a magnitude of 3 and B has a magnitude of 2, then R has a magnitude of 3 + -2 = 1.
This is very important. In physics a negative number does not always mean a smaller number. Mathematically –2 is smaller than +2, but in physics these numbers have the same magnitude (size), they just point in different directions (180° apart).
There are two methods of adding vectors:
1. Parallelogram:
A + B
A – B
2. Tip to Tail
A + B
A – B
It is readily apparent that both methods arrive at the exact same solution since either method is essentially a parallelogram. It is useful to understand both systems. In some problems one method is advantageous, while in other problems the alternative method is superior.
e. Draw the resultant vector using the parallelogram method of vector addition. You can answer these on this page.
Example: / a.b. / c.
d. / e.
Direction: What does positive or negative direction mean? How is it referenced? The answer is the coordinate axis system. In physics a coordinate axis system is used to give a problem a frame of reference. Positive direction is a vector moving in the positive x or positive y direction, while a negative vector moves in the negative x or negative y direction. This also applies to the z direction, which will be used sparingly in this course.
What about vectors that don’t fall on the axis? You must specify their direction using degrees measured from one of the four axes (-x, +x, -y, +y; or E, N, S, and W).
Component Vectors
A resultant vector is a vector resulting from the sum of two or more other vectors. Mathematically the resultant has the same magnitude and direction as the total of the vectors that compose the resultant. Could a vector be described by two or more other vectors? Would they have the same total result? This is the reverse of finding the resultant. You are given the resultant and must find the component vectors on the coordinate axis that describe the resultant.
Any vector can be described by an x axis vector and a y axis vector which summed together mean the exact same thing. The advantage is you can then use plus and minus signs for direction instead of the angle.
f. For the following vectors draw the component vectors along the x and y axis. You can answer on this page.