Your new designer chair has an S-shaped tubular metal frame that behaves just like a spring. When your friend, who weighs 580 N, sits on the chair, it bends downward 5 cm. What is the spring constant for this chair?
11600
To find the spring constant for the chair, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed.
Hooke's Law formula is: F = -kx
Where:
F is the force exerted by the spring
k is the spring constant
x is the displacement from the equilibrium position
In this case, when your friend sits on the chair, it bends downward 5 cm (which is equivalent to 0.05 meters), and the force exerted by your friend's weight is 580 N.
So we can rewrite the formula as:
580 N = -k * 0.05 m
To solve for k, divide both sides of the equation by -0.05 m:
k = -580 N / -0.05 m
Simplifying this expression, we get:
k = 11,600 N/m
Therefore, the spring constant for the chair is 11,600 N/m.
F=kx
k= F/x=580N/.05m=you do it.