Question

Infants enjoy bouncing from a seat that hangs by a spring attached to the top of a door frame. The infant learns to bounce up and down in simple harmonic motion. Suppose the total mass of an infant and the chair is 12.0 kg and that the spring has a k value of 1850 N/m. What is the spring's stretch when it comes to equilibrium with the child in the chair?

Answer 1

To calculate the spring's stretch when it comes to equilibrium with the child in the chair, we can use Hooke's Law. The spring's stretch is approximately 0.064 m.

Step-by-step explanation:

To calculate the spring's stretch when it comes to equilibrium with the child in the chair, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance the spring is stretched or compressed. The formula for Hooke's Law is F = -kx, where k is the spring constant and x is the displacement from the equilibrium position.

In this case, the force exerted by the spring is equal to the weight of the child and chair, which is mg, where m is the mass of the child and chair and g is the acceleration due to gravity (approximately 9.8 m/s²).

Therefore, we can set up the equation -kx = mg and solve for x to find the spring's stretch when it comes to equilibrium:

1. Substitute the given values into the equation: -kx = mg, k = 1850 N/m, m = 12.0 kg, g = 9.8 m/s²
2. Rearrange the equation to solve for x: x = -(mg / k)
3. Plug in the values: x = -((12.0 kg)(9.8 m/s²) / 1850 N/m)
4. Calculate the spring's stretch: x ≈ -0.064 m

Therefore, the spring's stretch when it comes to equilibrium with the child in the chair is approximately 0.064 m.