Physics H
Physics I Name ________________________
Physics I
1. What is the difference between dimensions and units?
2. What are the fundamental dimensions and their corresponding units in the SI system?
3. Give three examples of derived dimensions and their corresponding SI units.
4. What is a measurement? How is it different from a number?
Complete the following table:
Dimension SI unit (MKS) ____cgs unit _________H*_Common (B/E) unit_
Mass (M) __________ _________ ___________
___________ s _________ ___________
___________ __________ _________ ft
___________ __________ cm3 ___________
Velocity (L/T) m/s _________ ___________
Determine the following – NO CALCULATORS
If units are being added or subtracted, they must be the same (and that includes any metric prefix). Unlike units can be multiplied or divided.
1. 2 m x 4 m = ______ 6. 8 m2 / 2 m = _____
2. 4 km + 7 cg = ______ 7. 9 km / 3s = _____
3. 9 km + 12 km = ______ 8. 12 km / 4 kg = _____
4. 5 km / sec = ______ 9. 5 mm x 2 mm x 3 mm = _____
5. 8 cs – 2 ms = ______ 10. 8 kg x 2 m / 4 s2 = ________
(which operation do you do first?)
H* 11. 1012 kg x 1014 kg / 103 m2 = _____ 12. 2 x 104 kg + 2 x 103 g = _____
Convert each to the unit indicated: show your work
1) 25 m/s ______________ km/hr 4) 1.0 m2 ______________cm2
2) 70 km/hr ______________ m/s 5) 8.32 cm3 ______________ m3
3) 1.0 yr ______________ s
H* 6) 4.8 g/cm3 ________ kg/m3
7) 30 mi/hr ______________ m/s
Problem Solving:
1) A back yard is 5.9 m long and 7.5 m wide. 2) The radius of a circle is 5.5 cm,
a. What is the circumference in meters?
What length of fence will enclose the yard?
How much sod will cover the yard? b. What is its area in square meters?
3) Units will help you work this problem:
A wooden block has dimensions of 2.0 cm x 30 mm x (4.0 x 10-2 m).
It has a density of 0.60 g/cm3
a) What is the area of the largest face?
b) What is the volume of the block?
c) What is the mass of the block of wood?
GEOMETRY/TRIGONOMETRY
Line B touches the circle at a single point. Line A extends through the center of the circle.
a. What is line B in reference to the circle?
__________________________
b. How large is the angle between lines A and B?
_______________
What is the value of angle C? _______________
What is angle θ ? _______________
Using right triangle trigonometry and the Pythagorean Theorem solve the following. Your calculator must be in degree mode. SHOW ALL YOUR WORK! Remember: SOH CAH TOA
sin θ = opp / hyp cos θ = adj / hyp tan θ = opp / adj
[pic]
1) θ = 55o and c = 32 m, solve for a and b.
2) θ = 45o and a = 15 m/s, solve for b and c.
3) b = 17.8 m and θ = 65o, solve for a and c.
EQUATIONS
[pic]It is often helpful to solve problems for the unknown variable first – then substitute the numerical values. Solve each equation for the variable indicated. Show ALL your work leading to the answer.
F = ma solve for a: T = 2π [pic] solve for g:
a = vf – vo solve for vf: [pic] solve for v:
t
K = [pic]kx2 solve for x:
H*-
v2 = v02 + 2a(s – so) solve for a: [pic] solve for B:
INTERPRETING GRAPHS
In laboratory investigations, you generally control one variable and measure the effect it has on another variable while you hold all other factors constant. There are three relationships that occur frequently in physics:
[pic]
Graph A: If the dependent variable varies directly with the independent variable, the graph will
be a straight line
Graph B: If y varies inversely with x, the graph will be a hyperbola.
Graph C. If y varies directly with the square of x, the graph is a parabola.
1. Suppose you recorded the following data during a study of the relationship of force and acceleration. Prepare a graph showing these data.
|Force |Acceleration |
|(N) |(m/s2) |
|10 |6.0 |
|20 |12.5 |
|30 |19.0 |
|40 |25.0 |
[pic]
a. Describe the relationship between force and acceleration as shown by the graph.
b. What is the slope of the graph? Remember to include units with your slope. (1 N: 1 kg.m/s2)
c. What physical quantity does the slope represent? (use units to figure this out)
d. Write an equation for the line. _________________________________________
e. What is the value of the force for an acceleration of 15 m/s2?
f. What is the acceleration when the force is 50.0 N?
2. The following data show the distance an object travels in certain time periods. Prepare a graph showing these data.
|Position (m) |Time (s) |
|0 |0 |
|2 |1 |
|8 |2 |
|18 |3 |
|32 |4 |
|50 |5 |
[pic]
a. Describe the relationship between x and y and write a general equation for the curve.
b. Is the distance traveled greater between 0 s and 1 s or 3 s and 4 s?
c. Is the slope of the curve greater between 1 s and 2 s or 3 s and 4 s?
Honors Only DIMENSIONAL CONSISTENCY –
Any valid formula must be “dimensionally consistent”. That is, each side of the equal sign must have the same unit. For example: Given [pic] where x is in meters, v is in meters per second and t is in seconds. Replacing the variables with the units symbol produces m = m + (m/s)s. The “s” cancels leaving m = m + m which has m on both sides and is dimensionally consistent.
1. [pic] where x is in meters, v in meters per second, t in second and
a (acceleration) in meters per second squared
2. The time [pic]required for one complete oscillation of a mass [pic]on a spring of force constant
[pic] is: [pic] . Find the dimensions [pic] must have for this equation to be
dimensionally correct.
-----------------------
B
A
C
45o
30o
30o
θωε
................
................
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