Recitation Week 1
Chapter 1
Problem 1.10. Newton’s law of universal gravitation is represented by
F =
GM m
r2
(1)
where F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the
objects, and r is a distance. Force has the SI units kg·m/s2 . What are the SI units of the proportionality constant G?
GM m
r2
kg2
kg·m/s2 = G 2
m
G = m3 /kg·s2
F =
(2)
(3)
(4)
Problem 1.11. Kinetic energy K (Chapter 7) has dimensions kg·m2 /s2 . It can be written in terms of the momentum p
(Chapter 9) and mass m as
p2
K=
(5)
2m
(a) Determine the proper units for momentum using dimensional analysis. (b) The unit of force is the newton N, where
1 N = 1 kg·m/s2 . What are the units of momentum p in terms of a newton and another fundamental SI unit?
(a)
p2
2m
p2
2 2
kg·m /s =
kg
kg2 ·m2
p2 =
s2
p = kg·m/s
(9)
p = kg·m/s = kg·m/s2 · s = N·s
(10)
K=
(6)
(7)
(8)
(b)
Problem 1.13. A rectangular building lot has a width of 75.0 ft and a length of 125 ft. Determine the area of this lot in
square meters.
A = 75.0 ft · 125 ft ·
1m
3.28 ft
2
= 871 m2
(11)
Problem 1.15. A solid piece of led has a mass of 23.94 g and a volume of 2.10 cm3 . From these data, calculate the density
of lead in SI units (kilograms per cubic meter).
m
23.94 g
1 kg
ρ=
=
· 3 ·
3
V
2.10 cm 10 g
102 cm
1m
3
= 11, 400 kg/m3
(12)