Answer: So, the stiffness of the spring is
100
,
000
N/m
100,000N/m.
Explanation:To calculate the stiffness of the spring (also known as the spring constant), we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law equation is:
�
=
�
�
F=kx
Where:
�
F is the force exerted by the spring (in Newtons, N),
�
k is the spring constant or stiffness (in Newtons per meter, N/m),
�
x is the displacement from the equilibrium position (in meters, m).
Given that the work done in compressing the spring is 200 J and the displacement
�
x is 0.2 cm (which needs to be converted to meters), we can rearrange Hooke's Law to solve for the spring constant
�
k:
�
=
�
�
k=
x
F
First, let's convert the displacement from centimeters to meters:
�
=
0.2
cm
=
0.2
×
1
0
−
2
m
=
0.002
m
x=0.2cm=0.2×10
−2
m=0.002m
Now, we can calculate the spring constant:
�
=
�
�
=
200
N
0.002
m
k=
x
F
=
0.002m
200N
�
=
200
0.002
N/m
k=
0.002
200
N/m
�
=
100
,
000
N/m
k=100,000N/m
