Answer :
A spring has a rate of 159 lb/in. and is subjected to an impact loading coming from a 50 lb rigid body that is dropped from a height of 6 in. from the free end of the spring. he maximum load absorbed by the spring is approximately 966.4 lb.
To find the maximum load absorbed by the spring, we can calculate the change in potential energy of the rigid body as it falls and converts into potential energy of the compressed spring.
The potential energy of an object at a certain height is given by the formula:
PE=m⋅g⋅h
Where:
PE is the potential energy
m is the mass of the object
g is the acceleration due to gravity
h is the height of the object
Given information:
Mass of the rigid body, mm, is 50 lb
Height, h, is 6 in
Acceleration due to gravity, g, is approximately 32.174 ft/s²
First, let's convert the height from inches to feet:
h=612=0.5h=126=0.5 ft
Now, we can calculate the potential energy of the rigid body as it falls:
PE=50⋅32.174⋅0.5PE
PE≈805.85PE
The potential energy of the rigid body is converted into potential energy stored in the compressed spring. We can use Hooke's Law to relate the potential energy stored in the spring to the maximum load absorbed by the spring.
Hooke's Law states:
PE=12⋅k⋅x2PE
Where:
PE is the potential energy stored in the spring
k is the spring rate
x is the displacement of the spring
Given information:
Spring rate, k, is 159 lb/in
Rearranging the equation, we have:
x=2⋅PEkx
Substituting the values, we get:
x=2⋅805.85159x
x≈6.073x≈6.073 in
The displacement of the spring, xx, represents the maximum compression of the spring. The maximum load absorbed by the spring is equal to the spring rate multiplied by the displacement:
Load=k⋅x
Substituting the values, we have:
Load=159⋅6.073
Load≈966.387
Rounding the maximum load absorbed by the spring to 4 significant figures, we get:
Load≈966.4
Therefore, the maximum load absorbed by the spring is approximately 966.4 lb.
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