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# Work, Kinetic Energy and Potential Energy

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6.2. WORKED EXAMPLES
133
6.2
Worked Examples
6.2.1
Kinetic Energy
1. If a Saturn V rocket with an Apollo spacecraft attached has a combined mass
of 2.9 × 10
5
kg and is to reach a speed of 11.2
km
s
, how much kinetic energy will it
then have?
[HRW5 7-1]
(Convert some units first.) The speed of the rocket will be
v = (11.2
km
s
)
10
3
m
1 km
= 1.12 × 10
4 m
s
.
We know its mass: m = 2.9 × 10
5
kg. Using the definition of kinetic energy, we have
K =
1
2
mv
2
=
1
2
(2.9 × 10
5
kg)(1.12 × 10
4 m
s
)
2
= 1.8 × 10
13
J
The rocket will have 1.8 × 10
13
J of kinetic energy.
2. If an electron (mass m = 9.11 × 10
-31
kg) in copper near the lowest possible
temperature has a kinetic energy of 6.7×10
-19
J, what is the speed of the electron?
[HRW5 7-2]
Use the definition of kinetic energy, K =
1
2
mv
2
and the given values of K and m, and
solve for v. We find:
v
2
=
2K
m
=
2(6.7 × 10
-19
J)
(9.11 × 10
-31
kg)
= 1.47 × 10
12 m
2
s
2
which gives:
v = 1.21 × 10
6 m
s
The speed of the electron is 1.21 × 10
6 m
s
.
6.2.2
Work
3. A floating ice block is pushed through a displacement of d = (15 m)i - (12 m)j
along a straight embankment by rushing water, which exerts a force F = (210 N)i-
(150 N)j on the block. How much work does the force do on the block during the
displacement?
[HRW5 7-11]
Here we have the simple case of a straight­line displacement d and a constant force F.
Then the work done by the force is W = F · d. We are given all the components, so we can
compute the dot product using the components of F and d:
W = F · d = F
x
d
x
+ F
y
d
y
= (210 N)((15 m) + (-150 N)(-12 m) = 4950 J

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Summary :

## Using the definition of kinetic energy, we have K = 1 2 mv 2 = 1 2 (2.9 × 10 5 kg)(1.12 × 10 4 m s ) 2 = 1.8 × 10 13 J The rocket will have 1.8 × 10 13 J of kinetic energy. We find: v 2 = 2K m = 2(6.7 × 10 -19 J) (9.11 × 10 -31 kg) = 1.47 × 10 12 m 2 s 2 which gives: v = 1.21 × 10 6 m s The speed of the electron is 1.21 × 10 6 m s .

Tags : energy,kinetic,speed,force,hae,mass,work,block,hrw5,electron,displacement,rocket,112
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