Two identical 1.60 {\rm kg} masses are pressed against opposite ends of a spring of force constant 1.85 {\rm N}/{\rm cm}, compressing the spring by 25.0 {\rm cm} from its normal length.
I have no idea what your {\rm symbol means in fronnt of the various dimensions
To find the potential energy stored in the spring when it is compressed by 25.0 cm, we can use the formula for potential energy in a spring:
U = (1/2)kx^2
where:
U is the potential energy stored in the spring,
k is the force constant of the spring, and
x is the displacement of the spring from its normal length.
In this case, the force constant is given as 1.85 N/cm, and the displacement is 25.0 cm.
First, we need to convert the units of the force constant to N/m, since the displacement is given in meters:
1 N/cm = 100 N/m
So, the force constant (k) becomes 185 N/m.
Now, we can substitute the values into the formula:
U = (1/2)(185 N/m)(0.25 m)^2
Simplifying further:
U = (1/2)(185 N/m)(0.0625 m^2)
U = 5.78 J
Therefore, the potential energy stored in the spring when it is compressed by 25.0 cm is 5.78 Joules.