An ideal spring with a force constant (spring constant) of 15 N/m is initially compressed by 3.0 cm from its uncompressed position. How much work is required to compress the spring an additional 4.0 cm?

Potential Energy of the compressed string at x=3.0cm:

W = (1/2)*k*x^2

where k = spring constant = 15 N/m
x = distance = 3.0 cm

W = (1/2)*15*3^2
W = 67.5

Total work:
W_t = (1/2)*k*x^2

where x = 4+3 = 7

W_t= (1/2)*15*7^2
W_t = 367.5

W_t - W = 367.5 - 67.5

Work needed for the additional 4 cm is

300 J

Whoops, I think my units are off because since

k is measured in N/m I need to convert cm to m

Answer should be .03 Joules

Ty

Well, let's spring into action and calculate the work required, shall we?

To find the work done on a spring, we can use the formula:

Work = (1/2) * k * x^2

Where:
k is the spring constant (force constant) = 15 N/m
x is the displacement from the equilibrium position.

Now, let's calculate the work needed to compress the spring an additional 4.0 cm:

Work = (1/2) * 15 N/m * (0.04 m)^2

Calculating this, we get:

Work = 0.012 N∙m

So, it would take about 0.012 N∙m of work to compress the spring an additional 4.0 cm. Remember, just a little "spring" in your step can go a long way!

To find the work required to compress the spring an additional 4.0 cm, we can use the formula for elastic potential energy stored in a spring, which is:

Elastic potential energy = (1/2) * k * x^2

Where:
k = spring constant
x = displacement from the equilibrium position

In this case, the spring constant (k) is given as 15 N/m, and the displacement (x) is 4.0 cm.

First, we need to convert the displacement from centimeters to meters:
4.0 cm = 4.0 * 0.01 m = 0.04 m

Now, we can calculate the work required using the formula mentioned above:
Elastic potential energy = (1/2) * k * x^2
= (1/2) * 15 N/m * (0.04 m)^2
= (1/2) * 15 N/m * 0.0016 m^2
= 0.012 N*m
= 0.012 Joules

Therefore, the work required to compress the spring an additional 4.0 cm is 0.012 Joules.