When a 1.53-kilogram mass is placed on a spring
with a spring constant of 30.0 newtons per meter,
the spring is compressed 0.500 meter. How
much energy is stored in the spring?
To calculate the energy stored in a spring, we can use the formula:
E = (1/2) * k * x^2
where:
E is the energy stored in the spring,
k is the spring constant, and
x is the displacement of the spring.
Given:
Mass (m) = 1.53 kilograms
Spring constant (k) = 30.0 newtons per meter
Displacement (x) = 0.500 meter
Substituting the values into the formula:
E = (1/2) * k * x^2
= (1/2) * 30.0 * (0.500)^2
= (1/2) * 30.0 * 0.25
= 3.75 joules
Therefore, the energy stored in the spring is 3.75 joules.
To calculate the energy stored in a spring, we can use the formula:
E = (1/2) k x^2
Where:
E is the energy stored in the spring
k is the spring constant
x is the displacement of the spring from its equilibrium position.
In this case, the given values are:
k = 30.0 newtons per meter (N/m)
x = 0.500 meter
We can now substitute these values into the formula to find the answer.
E = (1/2) * 30.0 N/m * (0.500 m)^2
First, square the value of x: (0.500 m)^2 = 0.250 m^2
Next, multiply the spring constant by the squared displacement: 30.0 N/m * 0.250 m^2 = 7.50 Nm
Finally, multiply the result by 1/2 to find the energy stored in the spring:
E = (1/2) * 7.50 Nm = 3.75 Joules
Therefore, the energy stored in the spring is 3.75 Joules.
k=30 N/m
x=0.5 m
E=kx²/2