I have a task with a 12kg crate on a conveyor belt moving at u = 2.5m/s onto a ramp with kinetic friction uk = 0.3. The ramp is 3m long and I need to plot velocity against a range of angles then find the smallest angle for the ramp where the crate will still fall off at the end (s = 3).
I've been using angles from 0 to 30: A = linspace(0,30,301)
Then using this to get the normal force which seems to give correct values: N = m*g*cosd(A)
From this calculate the acceleration which also seems to give correct values: 12a = mgsinA - uk N -> a = (m*g*sind(A)-uk*N)/12
Then find the velocity using: v^2 = u^2 + 2as -> v = sqrt(u^2 + 2*a*s)
This gives imaginary values (e.g. 0.000 + 2.8267i) which I'm guessing due to this value being negative and then square root as the crate would realistically stop before reaching 3m. The values from 12.8 deg seem correct and don't have any imaginary parts.
When plotting A against v the velocity is 0 (as imaginary parts are ignored) until 10.8 when it starts to increase. At 10.8 deg the v value is 0.0000 + 0.2568i and at 10.9 deg it's 0.2018 + 0.0000i. When I've calculated it manually I get 22.6 degrees so unsure where I'm going wrong.
Any help is much appreciated!