Exam 1
Problem 1
Description:
Anna walks 160 m due north, 50 m due east, and then 45 m due south.
Part A
What is the magnitude of her net displacement?
ANSWER:
Part B
What is the direction of her net displacement?
ANSWER:
Problem 2
Description:
(a) How many inches does light travel in 4.0 nanoseconds? The speed of light is 3.0 x
10
8
(m/s).
Part A
ANSWER:
Problem 3
Description:
Short quantitative problem on dimensional analysis.
In physics, every physical quantity is measured with respect to a
unit
. Time is measured in seconds,
length is measured in meters, and mass is measured in kilograms. Knowing the units of physical
quantities will help you solve problems in physics.
Part A
Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on
the ground and causes the moon to orbit the earth. The force of gravitational attraction is
represented by the equation
,
where F is the magnitude of the gravitational attraction on either body,m
1
and m
2
are the masses of
the bodies, r is the distance between them, and G is the gravitational constant. In SI units, the units
or force are kg m/s
2
, the units of mass are kg, and the units of distance are m. For this equation to
have consistent units, the units of Gmust be which of the following?
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Part B
One consequence of Einstein's theory of special relativity is that mass is a form of energy. This
massenergy relationship is perhaps the most famous of all physics equations:
,
where m is mass, c is the speed of the light, and E is the energy. In SI units, the units of speed are
m/s. For the preceding equation to have consistent units (the same units on both sides of the
equation), the units of E must be which of the following?
ANSWER:
To solve the types of problems typified by these examples, we start with the given equation. For
each symbol whose units we know, we replace the symbol with those units. For example, we replace
m with kg. We now solve this equation for the units of the unknown variable.
Problem 4
Description:
Problems in unit conversion: one based importing goods and another on the Mars
Climate Orbiter .
Unit conversion problems can seem tedious and unnecessary at times. However, different systems of
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 Summer '09
 BACON

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