posted by Lindsay on .
A small steel ball bearing with a mass of 24 g is on a short compressed spring. When aimed vertically and suddenly released, the spring sends the bearing to a height of 1.23 m. Calculate the horizontal distance the ball will travel if the same spring is aimed 27° from the horizontal.
For this problem, does the mass need to be considered? Or do I just ignore the mass and solve for the velocities?
Yes, the mass has to be considered. The spring is operating against gravitational forces in the vertical.
energy in spring= massball*g*height
because it is short, you can ignore the change in GPE when the spring is compressed.
If that is so, then
1/2mv^2=mgh and you are right, mass divides out.
v initial= sqrt (2gh)
this is the same v initial when launched at any other angle.
Once I then have the initial vel., how can I go about getting the horizintal distance? Don't I need time?
initial vertical velocity= v*sinTheta
That will lead to time in air.
Ahh ok I got it now.