Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed 0.55 cm , its potential energy is 0.0020 J

a.What is the force constant of the spring? i found the fist answer is 130N/M

B. What compression is required for the spring potential energy to equal 0.0079 J ? pls help part with b

Oh, springs and their potential energy! They can really spring up some interesting questions, can't they? Alright, let's tackle part B!

To find out the compression required for the spring potential energy to equal 0.0079 J, we can use the equation for potential energy stored in a spring:

Potential Energy = (1/2) * k * x^2

Where k is the force constant of the spring (which we need to find) and x is the compression of the spring.

Given that the potential energy is 0.0079 J, we can set up the equation:

0.0079 J = (1/2) * k * x^2

Now, we can solve this equation for x, the compression. But since we're Clowns, let's throw in some fun and solve it step-by-step:

0.0079 J = (1/2) * k * x^2

0.0158 J = k * x^2 (Doubled it to keep things simple!)

k * x^2 = 0.0158 J

x^2 = 0.0158 J / k

x = √(0.0158 J / k)

Oops, it seems we can't solve for x without knowing the value of k! So, what do we do? Well, luckily we already found k in the previous part of the question, didn't we? It was 130 N/m!

So, now we can use that value of k:

x = √(0.0158 J / 130 N/m)

x ≈ √(0.00012 m^2)

x ≈ 0.011 m (approximately)

Therefore, the compression required for the spring potential energy to equal 0.0079 J is approximately 0.011 meters.

Hope that puts a spring in your step! Keep on compressing those springs, my friend!

To determine the compression required for the spring potential energy to equal 0.0079 J, we can use the formula for potential energy stored in a spring:

Potential energy = (1/2) * k * x^2

where k is the force constant of the spring and x is the compression of the spring.

We have already calculated the force constant of the spring to be 130 N/m. Now, we can rearrange the equation to solve for x:

x = sqrt((2 * Potential energy) / k)

Plugging in the given values, we have:

x = sqrt((2 * 0.0079 J) / 130 N/m)
x = sqrt(0.000121538) m
x ≈ 0.011 cm

Therefore, the compression required for the spring potential energy to equal 0.0079 J is approximately 0.011 cm.

To find the force constant of the spring, we can use the formula for potential energy stored in a spring:

Potential energy (PE) = 1/2 * k * x^2

Where:
PE = potential energy stored in the spring
k = force constant (also known as spring constant)
x = displacement/compression of the spring

In this case, we know that when the spring is compressed by 0.55 cm, its potential energy is 0.0020 J. Plugging these values into the formula, we can solve for k:

0.0020 J = 1/2 * k * (0.55 cm)^2

First, we need to convert the compression from centimeters to meters:

0.55 cm = 0.55 * 0.01 m = 0.0055 m

Now, we can rearrange the formula to solve for k:

k = (2 * PE) / x^2
k = (2 * 0.0020 J) / (0.0055 m)^2

k ≈ 130 N/m

So, the force constant of the spring is approximately 130 N/m.

Now, let's move on to part B.

We need to find the compression (x) required for the spring potential energy to equal 0.0079 J.

Using the same formula:

0.0079 J = 1/2 * k * x^2

Rearranging the formula to solve for x:

x^2 = (2 * PE) / k
x^2 = (2 * 0.0079 J) / 130 N/m

x^2 ≈ 0.000121 m^2

Taking the square root of both sides:

x ≈ √(0.000121 m^2)

x ≈ 0.011 m

Therefore, the compression required for the spring potential energy to equal 0.0079 J is approximately 0.011 meters.

PE=1/2 kx^2

.0020=1/2 k (.055^2)
solve for k

b. PE is directly proportional to the saqaure of compression, so

.0079/.0020 = (x/.55cm)^2
x in cm= .55cm * sqrt(.0079/.0020 )