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.