Question

If a 15mg insect flew into a web at speed 2.5m/s, how big of a deflection would the web make from its equilibrium position?
(spring constant that I had calculated was 1.48kg/s^2)

How should I approach this question and what equations should I use?

Answer 1

Normally k is in Newtons/meter
F = k x
your units do work, but only if you put g in there somehow.
perhaps you got k from hanging a weight on the spring ?
in that case and assuming g = 9.8 m/s^2
Force= m g = m in kg * 9.8 meters/s^2 = k * x meters
k = m in kg * 9.8 / x s^2
k = (m in kg * 9.8 m/s^2 / x meters
If that is what you did, then onward
F in Newtons = k x = 1.48 * x in meters
m a = F = 1.48 x
the work done on the web spring in stretch from 0 to Xf is (1/2) k X^2
that is the loss in kinetic energy of the insect (1/2) m v^2
so
k X^2 = m v^2
X= sqrt [ (mv*2) / k ]