Your new designer chair has an S-shaped tubular metal frame that behaves just like a spring with the spring constant 13000 N/m. When your friend, who weighs 940 N, sits on the chair, how far does it bend?
To determine how far the chair bends when your friend sits on it, we need to use Hooke's Law, which states that the extension of a spring is directly proportional to the force applied to it.
Hooke's Law equation is expressed as:
F = k * x
Where:
F is the force applied to the spring (in Newtons),
k is the spring constant (in N/m),
x is the displacement or change in length of the spring (in meters).
In this case, the force applied to the chair is the weight of your friend, which is 940 N. The spring constant, given in the problem, is 13000 N/m.
Using Hooke's Law, we can rearrange the equation to solve for x:
x = F / k
Now we can substitute the known values into the equation:
x = 940 N / 13000 N/m
Simplifying the equation:
x = 0.0723 m
Therefore, the chair bends approximately 0.0723 meters or 7.23 centimeters when your friend sits on it.