motion (1 Viewer)

[spikestar]

if i have mass a force vs time graph what can i do to find work?
thank you

 

[who_loves_maths]

this really should be in the Physics forum... but anyways, hope i didn't see this too late.

W(ork) = Int[F.dx] = Int[F.(dx/dt).dt] = Int[F.v.dt]

Given a graph of Force vs. Time, and knowing the equation of that graph (ie. Force as a function of time), then the area under the graph gives you the change in momentum of the particle. ie. integrating the graph gives you momentum as a function of time.
next, momentum = mv, so knowing the mass of the particle divide the momentum function throughout by 'm' to give velocity as a function of time.

then multiply the Force function and the velocity function to get F.v as a function of time.

and then integrate that function with respect to time to find net Work: W = Int[F.v.dt]


Hope this can still help in time

 

[who_loves_maths]

btw, if you are not already familiar with the equation W = Int[F.dx], where 'Int' is the integral sign, it's derived from the simple Newtonian relationship W = Fd = Fx, where 'd' or 'x' denotes the one dimensional displacement (not distance) of the particle.

So in the case where F is a non-constant function, you take infinitely small time-steps of F.delta(x), where the F at each infinitesimal time-step is considered as being constant, and sum them up - a Riemann sum.

Thus you end up with the Riemann integral expression for Work: W = Int[F.dx]