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?
They have given you more information than you need. Since they tell you the spring constant (k) and deflection (X), you don't need the weight (Mg) or mass, (M)
E = (1/2) k X^2 = (1/2)*30*(0.5)^2
= 3.75 Joules
To calculate the energy stored in a spring, you 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
In this case, the given values are:
k = 30.0 N/m (spring constant)
x = 0.500 m (displacement)
Substituting the values into the formula, we get:
E = (1/2) * 30.0 N/m * (0.500 m)^2
E = (1/2) * 30.0 N/m * 0.250 m^2
E = 0.375 Joules
Therefore, the energy stored in the spring is 0.375 Joules.
To calculate the amount of energy stored in a spring, you need to use Hooke's Law, which states that the amount of force exerted by a spring is directly proportional to the distance the spring is stretched or compressed. The formula can be written as:
E = (1/2) * k * x^2
Where:
E = energy stored in the spring
k = spring constant
x = displacement (compression or stretch) of the spring
In this case, you are given:
m = 1.53 kg (mass)
k = 30.0 N/m (spring constant)
x = 0.500 m (compression)
First, we need to calculate the force applied to the spring using Hooke's Law:
F = k * x
F = 30.0 N/m * 0.500 m
F = 15.0 N
Next, we can use the energy formula to find the amount of energy stored in the spring:
E = (1/2) * k * x^2
E = (1/2) * 30.0 N/m * (0.500 m)^2
E = 0.5 * 30.0 N/m * 0.250 m^2
E = 3.75 Joules
Therefore, the amount of energy stored in the spring is 3.75 Joules.