Answer:
a. spring constant = 125 N/m
b. This spring is less stiff than the one in Sample Problem A.
Explanation:
P.S - The Sample Problem A is as follows :
Given - Sample Problem A - A load of 45 N attached to a spring that is
Ā Ā Ā Ā Ā Ā hanging vertically stretches the spring 0.14 m. What is the spring
Ā Ā Ā Ā Ā Ā Ā constant?
Ā Ā Ā Ā Ā Ā Suppose the spring in Sample Problem A is replaced with a spring Ā
Ā Ā Ā Ā Ā Ā that stretches 36 cm from its equilibrium position.
To find - a. What is the spring constant in this case?
Ā Ā Ā Ā Ā Ā b. Is this spring stiffer or less stiff than the one in Sample Problem A.
Proof -
As given,
Load = 45 N
Amplitude = 0.14 m
Let the spring constant = k
As we know that,
Load = k (Amplitude)
ā45 = k(0.14)
āk = [tex]\frac{45}{0.14}[/tex] = 321.43
ā“ we get
Spring constant in Sample problem A = 321.43
Now,
a.)
Given, Amplitude = 36 cm = 0.36 m
Let the spring constant = kā
ā45 = kā (0.36)
ākā = [tex]\frac{45}{0.36}[/tex] = 125 N/m
b.)
AS we can see that kā Ā < k
ā This spring is less stiff than the one in Sample Problem A.
a. spring constant = 125 N/m
b. This spring is less stiff than the one in Sample Problem A.
The spring constant generally shows the stiffness of the spring and is the ratio of the force applied to the deflection of the spring.
It is given in the question that:
Sample Problem A - A load of 45 N attached to a spring that is
hanging vertically stretches the spring 0.14 m. Ā
Ā Ā Ā Ā Ā
Suppose the spring in Sample Problem A is replaced with a spring Ā
that stretches 36 cm from its equilibrium position.
a. What is the spring constant in this case?
As given,
Load F = 45 N
Amplitude Ā x= 0.14 m
Let the spring constant = k
As we know that spring force will be
[tex]F=k\times x[/tex]
[tex]45=k\times 0.14[/tex]
āk = 321.43N/m
ā“ we get
Spring constant in Sample problem A is Ā [tex]k=321.43\ \frac{N}{m}[/tex]
Now,
Given, Amplitude = 36 cm = 0.36 m
Let the spring constant = kā
ā45 = kā (0.36)
ākā= 125 N/m
b.) Is this spring stiffer or less stiff than the one in Sample Problem A.
AS we can see that kā Ā < k Ā new spring is less stiff than the one in Sample Problem A.
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