What are the roots of the polynomial equation? (picture below)
2 answers:
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The maximum compression of the spring is 0.276 m
Step-by-step explanation:
First of all, we calculate the spring constant of the spring, by using Hooke's law:
where
F = 10 kN = 10,000 N is the force applied
x = 1.25 cm = 0.0125 m is the corresponding compression of the spring
k is the spring constant
Solving for k,
When the truck impacts with the spring, all the kinetic energy of the truck is converted into elastic potential energy of the spring, so we can write
(1)
where
m is the mass of the truck
v = 2 m/s is the initial speed of the truck
is the spring constant
x is the compression of the spring
The mass of the truck can be found from its weight:
So now we can re-arrange eq.(1) to find the compression, x:
Learn more about kinetic energy:
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