A Mass Of 2.0kg Is Hung Off A Spring,which Extends 2cm. Determine The Energy Stored In The Spring.
Your answer is correct but you must approximate the gravity from 9.8 into 10m/s*2
Your answer is correct but you must approximate the gravity from 9.8 into 10m/s^2
assume g = 9.8 m/s^2
F = -k x
2 * 9.8 = k * .02
k = 980 Newtons
then
potential energy = U = (1/2) k x^2 = (1/2)(980)(.02)^2 Joules
Why assume gravity
Due to acceleration
Your answer is correct but why is you say F=-kx
To determine the energy stored in the spring, you need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law can be expressed as:
F = -kx
Where:
- F is the force exerted by the spring,
- k is the spring constant (a measure of the stiffness of the spring),
- x is the displacement from the equilibrium position.
In this case, the displacement is given as 2 cm, which we need to convert to meters before using it in the equation:
x = 0.02 m
Now, we need to determine the spring constant. The spring constant can be obtained by using the formula:
k = F / x
Since the mass of the object hanging on the spring is 2.0 kg, we can calculate the force exerted by gravity:
F = mg
Where:
- m is the mass of the object,
- g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the values:
F = 2.0 kg * 9.8 m/s^2
Once you have the force, you can use it to find the spring constant:
k = F / x
Now that we have the spring constant, we can calculate the energy stored in the spring using the formula for potential energy stored in a spring:
U = (1/2) * k * x^2
Substituting the values of k and x we found earlier, we can calculate the energy stored in the spring.