Question

An object of inertia 0.5kg is hung from a spring, and causes it to extend 5cm. In an elevator accelerating downward at 2 m/s^2 , how far will the spring extend if the same object is suspended from it? Draw the free body diagrams for both the accelerating and non-accelerating situations.

Answer 1

Answer:3.98cm

Explanation:

given data

mass of object$\left ( m\right )$=0.5kg

intial extension=5 cm

elevator acceleration=2 m/$s^2$

From FBD of intial position

Kx=mg

K=$\frac{0.5\times 9.81}{0.05}$

k=98.1 N/m

From FBD of second situation

mg-k$x_0$=ma

k$x_0$=m(g-a)

$x_0$=$\frac{0.5(9.81-2)}{98.1}$

$x_0$=3.98cm