1
Problem 1: Hooke’s Law
Description: Analyze the force of springs on Haitian taptaps as an application of Hooke’s law.
Learning
Goal: To understand the use of Hooke’s law for a spring. Hooke’s law states that the restoring force
F
on a
spring when it has been stretched or compressed is proportional to the displacement
x
of the spring from its
equilibrium position. The equilibrium position is the position at which the spring is neither stretched nor
compressed.
Recall that
F
∝
x
means that
F
is equal to a constant times
x
. For a spring, the proportionality constant
is called the spring constant and denoted by k. The spring constant is a property of the spring and must
be measured experimentally. The larger the value of k, the sti
ff
er the spring. In equation form, Hooke’s law
can be written
F
=
−
k
x
.
The minus sign indicates that the force is in the opposite direction to that of the spring’s displacement from
its equilibrium length and is "trying" to restore the spring to its equilibrium position. The magnitude of
the force is given by
F
=
kx
, where
x
is the magnitude of the displacement. In Haiti, public transportation
is often by taptaps, small pickup trucks with seats along the sides of the pickup bed and railings to which
passengers can hang on. Typically they carry two dozen or more passengers plus an assortment of chickens,
goats, luggage, etc. Putting this much into the back of a pickup truck puts quite a large load on the truck
springs.
A truck has springs for each wheel, but for simplicity assume that the individual springs can be treated as
one spring with a spring constant that includes the e
ff
ect of all the springs. Also for simplicity, assume that
all four springs compress equally when weight is added to the truck and that the equilibrium length of the
springs is the length they have when they support the load of an empty truck.
Part A A
60
−
kg
driver
gets into an empty taptap to start the day’s work. The springs compress
0
.
02m
. What is the e
ff
ective spring
constant of the spring system in the taptap?
Hint A.1
How to approach the problem: The compression of the springs is
governed by Hooke’s law. The amount the springs are compressed
when the driver climbs into the truck is given in the problem
statement. The force that acts to compress the springs is the
force caused by the driver getting into the truck.
F
=
−
k
x
solve for k
k
=
mag
(
F
)
mag
(
x
)
k
= 29000
ANSWER:
2
.
9
×
10
4
N
/
m
1.1
Part B
After driving a portion of the route, the taptap is fully loaded with a total of 25 people with an average
mass of
60kg
per person. In addition, there are three
15
−
kg
goats, five
3
−
kg
chickens, and a total of
25kg
of bananas on their way to the market. Assume that the springs have somehow not yet compressed to their
maximum amount. How much are the springs compressed?
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 Fall '07
 STANEK
 Force, Friction

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