A spring with a force constant of 4.5×104 N/m is initially at its equilibrium length. How much work must you do to stretch the spring 0.070 m?
How much work must you do to compress it 0.070 m?
(1/2)K X^2
With compression you use a negative X, but get the same answer as stretching by the same amount, because the X is squared.
K is the spring constant, 4.5*10^4.
Study, you must.
K is 4.5 x 10^4 = 45000. Use 0.03 as X
Well, stretching or compressing a spring sounds like a real "spring" challenge! But don't worry, I've got just the bouncy answer for you!
To calculate the work done on a spring, we can use the formula:
Work = (1/2)kx²
Where k is the force constant of the spring (4.5x10⁴ N/m) and x is the displacement (0.070 m).
So, to stretch the spring 0.070 m:
Work = (1/2) * (4.5x10⁴) * (0.070)²
And to compress the spring 0.070 m:
Work = (1/2) * (4.5x10⁴) * (-0.070)²
Remember to watch your sign when compressing the spring! Negative work is just the universe showing off its flexibility.
Now, let me do the math real quick. (Calculating. Calculating.) Voilà!
To stretch the spring 0.070 m, you would need to do approximately 139.13 joules of work. That's a sprightly little stretch!
And to compress the spring 0.070 m, you would need to do the same amount of work, approximately 139.13 joules. Just remember to embrace the negatives when compressing!
Hope that brought a little "spring" to your step!
To calculate the work done to stretch or compress a spring, we can use the formula:
Work = (1/2) * k * x^2
where:
- k is the force constant of the spring
- x is the displacement of the spring from its equilibrium position
Let's calculate the work done to stretch the spring first:
Given:
k = 4.5 × 10^4 N/m (force constant)
x = 0.070 m (displacement)
Substituting these values into the formula:
Work = (1/2) * (4.5 × 10^4 N/m) * (0.070 m)^2
Calculating this expression:
Work = (1/2) * (4.5 × 10^4 N/m) * (0.070 m * 0.070 m)
= (1/2) * (4.5 × 10^4 N/m) * 0.0049 m^2
= 110.25 N * m
= 110.25 J (Joules) (Joule is the unit of work)
So, the work done to stretch the spring by 0.070 m is 110.25 Joules.
Now, let's calculate the work done to compress the spring, which is the same magnitude but opposite in sign:
Work = -110.25 J
The negative sign indicates that work is done against the force of the spring.
Therefore, the work done to compress the spring by 0.070 m is -110.25 Joules.