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Physics 2211001, Fall 2008
Energy
Due at 11:00pm on Monday, September 29, 2008
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Problem 10.25
A 48.0
marble moving at 2.30
strikes a 30.0
marble at rest. What is the speed of each marble immediately
after the collision?
Part A
ANSWER:
=
0.531
m/s
Part B
=
2.83
m/s
Hooke's Law
Learning Goal:
To understand the use of Hooke's law for a spring.
Hooke's law states that the
restoring force
on a spring when it has been stretched or compressed is proportional to
the displacement
of the spring from its equilibrium position. The equilibrium position is the position at which the
spring is neither stretched nor compressed.
Recall that
means that
is equal to a constant times
. For a spring, the proportionality constant is called the
spring constant
and denoted by
. The spring constant is a property of the spring and must be measured
experimentally. The larger the value of
, the stiffer the spring.
In equation form, Hooke's law can be written
.
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
, where
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
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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 effect 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
driver gets into an empty taptap to start the day's work. The springs compress 0.02
. What is the effective
spring constant of the spring system in the taptap?
Hint A.1
How to approach the problem
Hint not displayed
Enter the spring constant numerically in newtons per meter.
ANSWER:
=
2.94
×
10
4
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 60
per person. In addition, there are three 15
goats, five 3
chickens, and a total of 25
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 '08
 DUNCAN
 Energy

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