Question

Your new designer chair has an S-shaped tubular metal frame that behaves like a spring with the spring constant 15100 N/m15100N/m. When your friend, who weighs 971 N971N, sits on the chair, how far does it bend?

a. 0.064 m
b. 0.082 m
c. 0.105 m
d. 0.121 m

Answer 1

The chair bends approximately 0.064 m when your friend sits on it.

Step-by-step explanation:

To determine how far the chair bends when your friend sits on it, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring. Let's denote the displacement as x. In this case, the weight of your friend, 971 N, is the force exerted on the chair. We can set up the equation as follows:

F = kx,

where F is the force exerted by the spring (971 N), k is the spring constant (15,100 N/m), and x is the displacement we want to find.

Plugging in the values, we get:

971 N = 15,100 N/m * x.

Solving for x, we find:

x = 0.064 m.

Therefore, the chair bends approximately 0.064 m when your friend sits on it.