Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed 0.54 cm, its potential energy is 0.0025 J.

(a) What is the force constant of the spring?
kN/m
(b) What compression is required for the spring potential energy to equal 0.0075 J?
cm

pe= 1/2 k x^2 solve for k

thank you. i just got it, but i can not seem to get part b.

would it be .0075=1/2*1714.7*x^2

To answer this question, we can use Hooke's Law, which states that the potential energy of a spring is directly proportional to the square of the displacement from its equilibrium position. The formula for potential energy stored in a spring is given by:

PE = (1/2) k x^2

where PE is the potential energy, k is the force constant of the spring (also known as the spring constant), and x is the displacement from the equilibrium position.

(a) To find the force constant of the spring, we can rearrange the formula and solve for k:

k = (2 * PE) / x^2

Given that the spring is compressed by 0.54 cm and its potential energy is 0.0025 J, we can substitute these values into the formula:

k = (2 * 0.0025 J) / (0.54 cm)^2

Now, let's convert cm to meters by dividing by 100:

k = (2 * 0.0025 J) / (0.54 m)^2

Simplifying the equation:

k = 0.009259 kN/m

Therefore, the force constant of the spring is 0.009259 kN/m.

(b) To find the compression required for the spring potential energy to equal 0.0075 J, we can rearrange the formula and solve for x:

x^2 = (2 * PE) / k

Substituting the given values:

x^2 = (2 * 0.0075 J) / (0.009259 kN/m)

Simplifying the equation:

x^2 = 161.29 m^2

Taking the square root of both sides:

x = √161.29 m

Now, let's convert meters to cm by multiplying by 100:

x ≈ 40.15 cm

Therefore, the compression required for the spring potential energy to equal 0.0075 J is approximately 40.15 cm.