Question

What is the kinetic energy of an arrow (m = 80 g) that is launched from a bowstring that is displaced 80 cm from rest and has a spring constant of 750 N/m? If it is fired straight up, at what height will it stop rising? Ignore friction.

Answer 1

Here energy stored in bowstring is converted into kinetic energy of arrow which in turn converted into gravitational potential energy of arrow

Kinetic energy =(kx^2)/2. (x^2 means x.x)

k=spring constant=750N/m

x=80cm=0.8m

Kinetic energy (E)=(kx^2)/2=(750x.8^2)/2=750x.8x.8/2=240joule

This kinetic energy is converted into gravitational potential energy

E=mgh

m=mass of arrow=80g=0.080kg

g=9.8m/s2

h=height reached

E=mgh

240=.08x9.8xh=.784h

h=240/.784=306.122meter