How much energy W needed to compress a spring from 15 cm to 10 cm if the constant of the spring is 150 N/m.
10-15=-5cm=-0.05m
0.5*150*(-0.05)^2=0.1875J
∆L=L¹ - L²
= 15cm - 10cm
= 5cm
= 0.05m
F= 150N X 0.05m
= 7.5N
W = FD
=7.5N X 0.05m
=0.375J
Well, let's spring into action and calculate that energy!
The potential energy stored in a spring can be calculated using the formula:
E = 1/2 * k * (x^2)
Where:
E is the potential energy
k is the spring constant
x is the displacement from the equilibrium position
So in this case, we have:
k = 150 N/m
x = (15 cm - 10 cm) = 5 cm = 0.05 m
Plugging these values into our formula, we get:
E = 1/2 * 150 N/m * (0.05 m)^2
Simplifying this equation gives us:
E = 1/2 * 150 N/m * (0.0025 m^2)
E = 0.1875 Joules
So, the energy required to compress the spring from 15 cm to 10 cm is approximately 0.1875 Joules. That's enough energy to make a spring-loaded clown nose pop right off your face!
To calculate the energy required to compress a spring, you can use the formula for the potential energy stored in a spring:
E = 1/2 * k * (x^2),
where:
E is the energy stored in the spring,
k is the spring constant (150 N/m in this case), and
x is the displacement of the spring from its equilibrium position (15 cm - 10 cm = 5 cm = 0.05 m).
Now, let's substitute the given values into the formula:
E = 1/2 * 150 N/m * (0.05 m)^2
Simplifying this expression:
E = 1/2 * 150 N/m * 0.0025 m^2
E = 0.1875 N * m = 0.1875 Joules.
Therefore, the energy needed to compress the spring from 15 cm to 10 cm is 0.1875 Joules.
d = 15-10 = 5 cm = 0.05 m.
F = 150N/m * 0.05m = 7.5 N.
Work = F*d = 7.5 * 0.05 = 0.375 Joules.