If a bungee rope has a spring constant of 60 N/m. How far will it extend (stretch) if a person who weighs 600N (60Kg) is placed on it?
To determine how far the bungee rope will extend when a person is placed on it, we can use Hooke's Law. Hooke's Law states that the stretch of a spring is directly proportional to the force applied to it.
The equation for Hooke's Law is:
F = -kx
Where:
F is the force applied to the spring (in Newtons),
k is the spring constant (in N/m), and
x is the distance the spring is stretched (in meters).
In this case, the force applied to the spring is the weight of the person, which is 600N. The spring constant is given as 60 N/m. We need to solve for x, which is the distance the bungee rope will extend.
So, let's rearrange the equation to solve for x:
x = -F / k
Substituting the given values:
x = -600N / 60 N/m
Simplifying the equation:
x = -10 m
The negative sign indicates the direction of the stretch. In this context, it means that the bungee rope will extend downwards by 10 meters when a person weighing 600N is placed on it.