show how you would you arrange to find f in terms of v,m and r from four equations below.
f=1/t, f=ma,v=2piR/T,a=v^2/R
Thanks
To find the expression for f in terms of v, m, and r from the given equations, we need to manipulate and substitute the equations in a way that isolates f.
1) Start with the equation f = 1/t.
2) From the equation f = ma, we can replace f in the first equation with ma: 1/t = ma.
3) Now, we can manipulate the equation a = v^2/r to solve for a in terms of v and r. By rearranging the equation, we get a = v^2/r.
4) Substitute this value of a into our equation from step 2: 1/t = m(v^2/r).
5) Next, let's work with the equation v = 2πR/T. We can rearrange it to get T = 2πR/v.
6) Substitute the value of T into the equation from step 4: 1/(2πR/v) = m(v^2/r).
7) Simplify the equation: v/(2πR) = m(v^2/r).
8) Cross multiply to eliminate the fractions: vr = 2πm(v^2).
9) Rearrange the equation to isolate f: f = (vr)/(2πm(v^2)).
So, the expression for f in terms of v, m, and r is f = (vr)/(2πm(v^2)).