Homework Problems
1. Carry out the following arithmetic operations:
(a) the sum of the measured values 756, 37.2, 0.83, and 2.5;
(b) the product 0.0032 x 356.3
(c) the product 5.620 x π.
(d) 3.42 × 25.4 + 2.32
3 .2
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 28
2. The population density of Los Angeles is about 4000
people/km2. That of San Francisco is about 6000
people/km2. How many times farther away is the average
person's nearest neighbor in LA than in San Francisco?
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 29
3. A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high
ceilings. What is the volume of the interior of the house in
cubic meters and in cubic centimeters?
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 30
4. For the triangle shown in this figure what are (a) the
length of the unknown side, (b) the angle θ, (c) the sine of
φ, and (c) the tangent of θ?
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 31
5. Estimate the number of Ping-Pong balls that would fit
into a typical-size room (without being crushed). In your
solution, state the quantities you measure or estimate and
the values you take for them.
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 32
6. What is the volume of your body in cubic centimeters?
Describe how you estimate this volume.
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 33
7. Analyze the dimensions for each of these equations. Are
they dimensionally correct?
a)
b)
c)
1 2 1
2
mv = mvo + mgh
2
2
xma = 12 mv 2
v = vo + at 2
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 34
8. Evaluate this derivative by two methods
d
(t − 2) 2
dt
a) Use the chain rule to find the result.
b) Use FOIL to expand the quadratic term and then find the
derivative.
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 35
9. Evaluate this integral
t =1
3
(
t
∫ − 4 + t )dt
t =0
General Physics I
Chapter 1, Units and Measurements, Calculus Review
Page 36