50kg drops from a height of 2meters straight down with a force constant of 8 x 1000n/m. What maximum distance does she compress?
To determine the maximum distance the weight compresses, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the distance it is compressed or extended.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force applied to the spring (in newtons),
k is the force constant (also known as the spring constant, in newtons per meter),
x is the distance the spring is compressed or extended (in meters).
In this scenario, the weight is dropping, and the force exerted by the spring is acting upwards against the weight. The force exerted by the spring is equal to the weight of the object, which can be calculated as:
F = m * g
Where:
m is the mass of the object (in kilograms),
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given:
m = 50 kg (mass of the object)
k = 8 x 1000 N/m (force constant)
g = 9.8 m/s^2 (acceleration due to gravity)
First, let's calculate the force exerted by the spring:
F = m * g
F = 50 kg * 9.8 m/s^2
F = 490 N
Now, we can rearrange Hooke's Law equation to solve for the maximum distance compressed:
F = k * x
Rearranging the equation, we have:
x = F / k
Substituting the values, we get:
x = 490 N / (8 x 1000 N/m)
x = 0.06125 m
Therefore, the weight will compress the spring by a maximum distance of approximately 0.06125 meters (or 6.125 centimeters).