AP Physics Summer assignment Problems
Show all work including formulas and units on another sheet
Read text chapters 1 and 2. Chapter 1 is pretty long winded, but may help you with some of the problems below.
Chapter 2 is where we start class in September. I will be giving you a quiz on this material when we convene in the
fall.
1. The distance to the Andromeda Galaxy is estimated at about 2 x106 light years. A light year is the distance
traveled by light in one year; if the speed of light is 3x 108 m/s, about how far is it from our galaxy to
Andromeda? (1 year = 3.15 x107 s)
2. A bird, accelerating from rest at a constant rate, experiences a displacement of 28 m in 11 s. What is the average
velocity?
3. A cheetah can run at approximately 100 km/hr and a gazelle at 80.0 km/hr. If both animals are running at full
speed, with the gazelle 70.0 m ahead, how long before the cheetah catches its prey?
4. A European sports car dealer claims that his car will accelerate at a constant rate from rest to 100 km/hr in 8.00 s.
If so, what is the acceleration? (Hint: First convert speed to m/s.)
5. A ball is pushed with an initial velocity of 4.0 m/s. The ball rolls down a hill with a constant acceleration of 1.6
m/s2. The ball reaches the bottom of the hill in 8.0 s. What is the ball’s velocity at the bottom of the hill?
6. A bird, accelerating from rest at a constant rate, experiences a displacement of 28 m in 11 s. What is its
acceleration?
7. Norma releases a bowling ball from rest; it rolls down a ramp with constant acceleration. After half a second it
has traveled 0.75 m. How far has it traveled after two seconds?
8. An automobile driver puts on the brakes and decelerates from 30.0 m/s to zero in 10.0 seconds. What distance
does the car travel?
9. A rock is thrown straight down with an initial velocity of 14.5 m/s from a cliff. What is the rock’s displacement
after 2.0 s? (Acceleration due to gravity is 9.80 m/s2.)
10. A rock is thrown straight up with an initial velocity of 24.5 m/s. What maximum height will the rock reach
before starting to fall downward? (Take acceleration due to gravity as 9.80 m/s2.)
11. A rock, released at rest from the top of a tower, hits the ground after 1.5 s. What is the speed of the rock as it hits
the ground? (g = 9.8 m/s2 and air resistance is negligible)
12. A basketball player can jump 1.6 m off the hardwood floor. With what upward velocity did he leave the floor?
13. Round the following numbers to two digits:
a. 40.523
b) 1.3511
c) 104.97055
c) 8.235
8
d) 2.751 x 10
e) 79.2588
f) 41.86632
g) 3.05
14. Round the following to one digit and write them in scientific notion.
h) 3.9814 x 105
i) 0.9114
j) 0.03765
k) 8.25
l) 22.494
m) 0.2056
n) 0.0045
o) 8.65
Answer in correct SIG FIG’s:
14. A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?
15. Mercury metal is poured into a graduated cylinder that holds exactly 22.5 mL. The mercury used to fill the cylinder
weighs 306.0 g. From this information, calculate the density of mercury.
16. What is the weight of the ethyl alcohol that exactly fills a 200.0 mL container? The density of ethyl alcohol is 0.789
g/mL.
17. A rectangular block of copper metal weighs 1896 g. The dimensions of the block are 8.4 cm by 5.5 cm by 4.6 cm.
From this data, what is the density of copper?
18. A flask that weighs 345.8 g is filled with 225 mL of carbon tetrachloride. The weight of the flask and carbon
tetrachloride is found to be 703.55 g. From this information, calculate the density of carbon tetrachloride.
19. Calculate the density of sulfuric acid if 35.4 mL of the acid weighs 65.14 g.
20. Find the mass of 250.0 mL of benzene. The density of benzene is 0.8765 g/mL.
21. A block of lead has dimensions of 4.50 cm by 5.20 cm by 6.00 cm. The block weighs 1587 g. From this information,
calculate the density of lead.
3.8 liters = 1 gallon
2.54 cm = 1 inch
2.2 lbs = 1 kg
1 meter = 0.000621371192 miles
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
Convert 3598 grams into pounds
Convert 3.7 kg into grams.
Convert 4500 mm into meters.
Convert 48900 g into kg.
Convert 0.75 cm into m.
Convert 2745 mm into km.
How many ng are there in 5.27 x 10-13 kg?
How many miles is a 10 kilometer running race?
How many kilometers is a marathon (26.2 miles)?
What is a metric ton in grams, kg, and pounds?
The Exxon Valdez spilled about 1 billion gallons of oil, how many liters is this?
The distance to the moon is 238,855 miles. How many meters is this?
Which is faster, 60 miles an hour or 60 feet a second?
Convert 35 liters to gallons.
36. The density of water at 4oC is known to be 1.00 g / mL. Kim experimentally found the density of water to be1.085 g
/ mL. What is her percent error?
37. An object has a mass of 35.0 grams. On Huey's balance, it weighs 34.92 grams. What is the percent error of his
balance?
38. Florence measured the volume of a cylinder and determined it to be 54.5 cm3. The teacher told her that she was
4.65% too high in her determination of the volume. What is the actual volume of the cylinder?
39. Barry gets a paper back in lab with " - 2.77 % error" written on it. He had found the mass of an object to be 100.3
grams. What should he have found as the mass of the object?
40. After lab, all of Henry's friends looked at his data and told him that he was 31.2% too low in the boiling point he had
recorded. He had recorded 50o on his data sheet. What is the correct boiling point of the liquid he was working with?
Algebra & Functions
A working knowledge of algebra is essential to success in physics. A direct proportion is a function whose graph is a nonhorizontal line that passes through the origin. y = kx ; k is the constant of proportionality A linear function has a graph
that is a non-horizontal line. y = mx + b; m is the slope of the line and b is the y-intercept. A direct proportion is a
special case of a linear function, where b = 0.
A quadratic function has a graph that is a parabola. When y is proportional to x2 , the graph goes through the origin and
has a slope that increases as x increases. y = ax2 + bx + c An inverse relation has a graph that is a hyperbola (in the first
quadrant). When y is proportional to 1/x, the graph is asymptotic to the x and y axes. y = k/x
Identify the variable relationships.
41. F = -kx, (F vs. x) This function is ___________________________________. K
represents the _____________________________ of the graph.
42. U = mgh, (U vs. h) This function is ___________________________________. mg
represents the _____________________________ of the graph
43. x = ½ at2 (x vs. t) This function is ____________________________________. Its
graph will look like ________________________________________________. If x is
graphed vs. t2 the slope will be ___________________________.
44. a=F/m (a vs. m). This function is ______________________________________. Its
graph will look like ___________________________________________________.
45.
46.
47.
48.
Plot a graph of the data shown in the table below.
Draw a line of best fit.
Calculate the slope of the line
Write an equation to represent the line.. If you like, you can use excel to do 45-48.
x
y
0
0.5
1
2
3
4
5
0
2
8
13
26
37
50
Consider the following equations:
i.
ii.
iii.
iv.
49.
50.
51.
52.
53.
54.
d=1/2at2 + vit
vf2 = vi2 + 2ad
n1sinθi = n2sinθ2
KE=1/2mv2
Solve equation ii for d (in other words, rearrange the formula so it says d=……)
Solve equation iv for m
Solve ii for vi
Sove i for t
Solve iii for θ2
The end.
Notes on Sig Figs:
There are three rules on determining how many significant figures are in a number:
1.
2.
3.
Non-zero digits are always significant.
Any zeros between two significant digits are significant.
A final zero or trailing zeros in the decimal portion ONLY are significant.
Please remember that, in science, all numbers are based upon measurements (except for a very few that are defined). Since all measurements are uncertain, we must only use those numbers that
are meaningful. A common ruler cannot measure something to be 22.4072643 cm long. Not all of the digits have meaning (significance) and, therefore, should not be written down. In science,
only the numbers that have significance (derived from measurement) are written.
Rule 1: Non-zero digits are always significant.
If you measure something and the device you use (ruler, thermometer, triple-beam balance, etc.) returns a number to you, then you have made a measurement decision and that ACT of
measuring gives significance to that particular numeral (or digit) in the overall value you obtain. Hence a number like 26.38 would have four significant figures and 7.94 would have three.
The problem comes with numbers like 0.00980 or 28.09.
Rule 2: Any zeros between two significant digits are significant.
Suppose you had a number like 406. By the first rule, the 4 and the 6 are significant. However, to make a measurement decision on the 4 (in the hundred's place) and the 6 (in the unit's place),
you HAD to have made a decision on the ten's place. The measurement scale for this number would have hundreds and tens marked with an estimation made in the unit's place. Like this:
Rule 3: A final zero or trailing zeros in the decimal portion ONLY are significant.
Here are two examples of this rule with the zeros this rule affects in boldface: 0.00500 & 0.03040
Here are two more examples where the significant zeros are in boldface: 2.30 x 10¯5 & 4.500 x 1012
What Zeros are Not Discussed Above:
Zero Type #1: Space holding zeros on numbers less than one.
Here are the first two numbers from just above with the digits that are NOT significant in boldface:
0.00500 & 0.03040
These zeros serve only as space holders. They are there to put the decimal point in its correct location. They DO NOT involve measurement decisions. Upon writing the numbers in scientific
notation (5.00 x 10¯3 and 3.040 x 10¯2), the non-significant zeros disappear.
Zero Type #2: the zero to the left of the decimal point on numbers less than one. When a number like 0.00500 is written, the very first zero (to the left of the decimal point) is put there by
convention. Its sole function is to communicate unambiguously that the decimal point is a decimal point. If the number were written like this, .00500, there is a possibility that the decimal point
might be mistaken for a period.
Zero Type #3: trailing zeros in a whole number.
200 is considered to have only ONE significant figure while 25,000 has two.
When whole number are written as above, the zeros, BY DEFINITION, did not require a measurement decision, thus they are not s ignificant. However, it is entirely possible that 200 really
does have two or three significant figures. If it does, it will be written in a different manner than 200. Typically, scientific notation is used for this purpose. If 200 has two significant figures,
then 2.0 x 102 is used. If it has three, then 2.00 x 102 is used. If it had four, then 200.0 is sufficient. See rule #2 above.
Zero Type #4: leading zeros in a whole number.
00250 has two significant figures. 005.00 x 10¯4 has three.
Exact Numbers: Exact numbers, such as the number of people in a room, have an infinite number of significant figures. Exact numbers are counting up how many of something are present,
they are not measurements made with instruments. Another example of this are defined numbers, such as 1 foot = 12 inches. There are exactly 12 inches in one foot. Therefore, if a number is
exact, it DOES NOT affect the accuracy of a calculation nor the precision of the expression. Some more examples:
There are 100 years in a century; 2 molecules of hydrogen react with 1 molecule of oxygen to form 2 molecules of water; and There are 500 sheets of paper in one ream. Interestingly, the
speed of light is now a defined quantity. By definition, the value is 299,792,458 meters per second.