If it requires 5.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 7.1 cm?
work = 1/2 kx^2
so, ((9.1/2.0)^2 - 1) * 5.0 = 98.5 J
Well, let me spring up with an answer for you! If it takes 5.0 J of work to stretch the spring by 2.0 cm, we can say that the work done is directly proportional to the displacement. So, if the displacement increases by 7.1 cm (which is about the length of a baby clown shoe), we can calculate the additional work required using a proportional relationship.
Using some clowntastic math, we can set up a ratio: 5.0 J / 2.0 cm = X J / 7.1 cm. Cross multiplying, we have 2.0 cm times X J equals 5.0 J times 7.1 cm.
Now, putting on my clown hat and doing some calculations, we have 2.0 cm times X J = 35.5 J cm. To find X, we divide both sides by 2.0 cm, giving us X J = 35.5 J cm / 2.0 cm.
Finally, dividing J cm by cm, our answer is X = 17.75 J. So, approximately 17.75 J of work will be required to stretch the spring an additional 7.1 cm. Just remember to stretch the spring carefully, or you might find yourself bouncing around like a dancing clown on a pogo stick!
To find out how much more work will be required to stretch the spring an additional 7.1 cm, we need to determine the spring constant first using the given information.
The spring constant (k) can be calculated using Hooke's Law:
F = kx
Where:
F is the force applied to the spring
k is the spring constant
x is the displacement from the equilibrium position
In this case, the work done (W) on the spring to stretch it by a certain displacement is given by:
W = (1/2)kx^2
Given:
W = 5.0 J
x = 2.0 cm = 0.02 m
From the formula, we can rearrange it to solve for k:
k = 2W / x^2
k = 2(5.0 J) / (0.02 m)^2
k = 2(5.0 J) / 0.0004 m^2
k = 250 J/m^2
Now, we can find the additional work required to stretch the spring by 7.1 cm.
x = 7.1 cm = 0.071 m
Using the formula:
W = (1/2)kx^2
W = (1/2)(250 J/m^2)(0.071 m)^2
W = (1/2)(250 J/m^2)(0.005041 m^2)
W = (1/2)(1.2675 J)
W ≈ 0.6338 J
Therefore, approximately 0.6338 Joules of work will be required to stretch the spring an additional 7.1 cm.
To find out how much more work is required to stretch the spring an additional 7.1 cm, we need to first determine the spring constant (k) of the spring. The spring constant is a measure of how stiff or soft the spring is.
The formula that relates the amount of work done on a spring to the displacement of the spring is given by:
W = (1/2) * k * x^2
Where:
W = Work done on the spring
k = Spring constant
x = Displacement of the spring
Given that it requires 5.0 J of work to stretch the spring by 2.0 cm, we can use this information to find the spring constant as follows:
5.0 J = (1/2) * k * (0.02 m)^2
Rearranging the equation, we can solve for k:
k = 5.0 J / ((1/2) * (0.02 m)^2)
Simplifying the calculation, we get:
k = 5.0 J / (0.005 m^2)
k = 1000 N/m
Now that we have the spring constant (k), we can calculate the additional work required to stretch the spring by an additional 7.1 cm.
First, convert the additional displacement to meters:
Additional displacement (x_additional) = 7.1 cm = 0.071 m
Using the formula for work done on a spring, we can calculate the additional work as follows:
W_additional = (1/2) * k * (x_additional)^2
Substituting the values we found:
W_additional = (1/2) * 1000 N/m * (0.071 m)^2
Simplifying the calculation, we get:
W_additional ≈ 2.55 J
Therefore, approximately 2.55 J of additional work will be required to stretch the spring an additional 7.1 cm.