A Mass of 2kg hung off a spring .which extend 2 cm determine the energy stored in the spring
the energy stored in the spring is the change
... in the gravitational P.E. of the mass
E = m g h = 2 * 9.8 * .02 Joules
To determine the energy stored in a spring, you need to use the formula for the potential energy of a spring. The potential energy stored in a spring is given by the equation:
Potential Energy = (1/2) * k * x^2
Where:
- k is the spring constant (measured in N/m, Newtons per meter)
- x is the displacement of the spring from its equilibrium position (measured in meters)
In this case, you are given that a mass of 2 kg is hung off the spring and it extends by 2 cm.
To find the spring constant (k), you need to know the restoring force exerted by the spring and the corresponding displacement. The restoring force of a spring is given by Hooke's Law:
Restoring Force = k * x
Since the spring is in equilibrium when no force is applied, we can equate the weight of the mass (F = m * g) to the restoring force of the spring:
m * g = k * x
Where:
- m is the mass (2 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- x is the displacement of the spring (2 cm or 0.02 m)
Solving this equation for the spring constant (k), we get:
k = (m * g) / x
k = (2 kg * 9.8 m/s^2) / 0.02 m
Now that we have the value of the spring constant (k), we can substitute it back into the formula for potential energy:
Potential Energy = (1/2) * k * x^2
Potential Energy = (1/2) * [(2 kg * 9.8 m/s^2) / 0.02 m] * (0.02 m)^2
Simplifying the expression, we get:
Potential Energy = (1/2) * (2 kg * 9.8 m/s^2) * (0.0004 m^2)
Potential Energy = 0.392 Joules
Therefore, the energy stored in the spring is 0.392 Joules.
F = kx ==> k = F/x
E = 1/2 kx^2 = 1/2 * F/x * x^2 = Fx/2 = mgx/2
watch the units