It takes 3.78 J of work to stretch a Hooke’s-law
spring 14.2 cm from its unstressed length.
How much the extra work is required to
stretch it an additional 11.2 cm?
Answer in units of J.
Now this is so similar to your last question that I hesitate to say aanything.
remember from the other one:
potential energy stored = (1/2) k x^2
so
3.78 Joules = .5 * k * (.142)^2
solve for k
now TOTAL work to get to 14.2 + 11.2 or 25.4
= .5 * k * (.254)^2 Joules
now subtract 3.78 from that
You are welcome.
Oh!! I get it, I just had trouble finding out how to solve to get k, but then I realized you just have to divide both sides until you isolate k by itself. Thanks!
Why did the spring go on a diet? It wanted to be extra stretchy!
To calculate the extra work required to stretch the spring an additional 11.2 cm, we can use the formula for work done on a spring:
W = (1/2) k x^2
Where W is the work done, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this case, we already know that it takes 3.78 J of work to stretch the spring 14.2 cm. We can use this information to find the spring constant:
3.78 J = (1/2) k (0.142 m)^2
Solving for k, we find:
k = (2 * 3.78 J) / (0.142 m)^2
Now we can use the spring constant to calculate the additional work required to stretch the spring 11.2 cm:
W_add = (1/2) k (0.112 m)^2
Now, let's put the numbers into the formula and calculate the extra work:
W_add = (1/2) (2 * 3.78 J / (0.142 m)^2) (0.112 m)^2
W_add = 1.59 J
Therefore, the extra work required to stretch the spring an additional 11.2 cm is 1.59 J. Keep on stretching, you're doing great!
To calculate the extra work required to stretch the spring an additional 11.2 cm, we need to make use of Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
Hooke's Law can be expressed as follows:
F = k * x
Where:
F = Force applied to the spring
k = Spring constant (a measure of the stiffness of the spring)
x = Displacement from the spring's unstressed length
Here, we are given the initial displacement, the work done to stretch the spring by 14.2 cm, and we are asked to calculate the additional work required to stretch it by an additional 11.2 cm.
First, let's calculate the initial force applied to the spring. We know that the work done on a spring is given by:
Work = (1/2) * k * x^2
Where:
Work = Work done on the spring
k = Spring constant
x = Displacement from the spring's unstressed length
Given that the work done is 3.78 J and the displacement is 14.2 cm, we can rearrange the equation to solve for the spring constant:
3.78 J = (1/2) * k * (0.142 m)^2
Simplifying this equation, we get:
k = 3.78 J / (0.5 * (0.142 m)^2)
Now that we have the spring constant, we can calculate the force required to stretch the spring an additional 11.2 cm. From Hooke's Law:
F = k * x
Given that the displacement is 11.2 cm, we can convert it to meters:
x = 11.2 cm = 0.112 m
Substituting the values into the equation, we have:
F = (spring constant) * (displacement) = k * x
F = k * x = (spring constant) * (0.112 m)
Calculating the spring constant k in the earlier step and substituting the value, we can calculate the force F.
Finally, we can calculate the additional work done to stretch the spring by multiplying the force by the displacement:
Additional work = F * x
This will give the extra work required to stretch the spring an additional 11.2 cm in units of J.