A single mass (m1 = 3.1 kg) hangs from a spring in a motionless elevator. The spring constant is k = 338 N/m.
What is the distance the spring is stretched from its unstretched length?
If I were to use the equation f=-kx what would that look like? or is that not the right equation to use
M*g = 3.1 * 9.8 = 30.38 N. = Wt. of the mass.
1m/338N * 30.38N. = 0.08988 m. = 9.0 cm.
To find the distance the spring is stretched from its unstretched length, you can use Hooke's Law equation, which relates the force exerted by a spring to the displacement it undergoes. The equation is given as:
F = -kx
where:
F = the force exerted by the spring
k = the spring constant
x = the displacement or stretch of the spring from its unstretched position
To find the distance the spring is stretched, we need to rearrange this equation to solve for x:
x = -F/k
In this case, the force exerted by the spring (F) can be calculated using the weight of the mass hanging from it. The weight (W) is given by:
W = mg
where: m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).
Plugging the values into the equations:
W = mg = 3.1 kg * 9.8 m/s² = 30.38 N
Now, substituting the calculated force into the equation for x:
x = -F/k = -(30.38 N) / (338 N/m) ≈ -0.09 m
The negative sign indicates that the spring is stretched in the opposite direction to the gravitational force. Therefore, the spring is stretched approximately 0.09 meters from its original length.