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Homework Statement
An object of mass m is constrained to move in a circle of radius r. Its tangential acceleration as a function of time is given by [tex]a_{tan} = b + ct^2[/tex], where b and c are constants.
A) If [tex]v = v_0[/tex] at t = 0, determine the tangential component of the force, [tex]F_{\tan }[/tex], acting on the object at any time t > 0.
Express your answer in terms of the variables m, r, [tex]v_0[/tex], b, and c.
B) Determine the radial component of the force [tex]F_{\rm{R}}[/tex].
Express your answer in terms of the variables m, r, [tex]v_0[/tex], b, t, and c.
Homework Equations
[tex]a_{tan} = b + ct^2[/tex]
[tex]a_r=\tfrac{v^2}{r}[/tex]
Newton's Laws
The Attempt at a Solution
A. was not a problem for me:
[tex]F_{\tan}=ma_{\tan}=m(b+ct^2)[/tex]
For B.:
[tex]F_R=ma_r[/tex]
[tex]a_r=\tfrac{v^2}{r}[/tex]
It seems to make sense that because v is tangential speed we could use...
[tex]v(t)=v_0+a_{\tan}t=v_0+(b+ct^2)t[/tex]
So that...
[tex]a_r=\frac{(v_0+(b+ct^2)t)^2}{r}[/tex]
Finally giving...
[tex]F_R=m(\frac{(v_0+(b+ct^2)t)^2}{r}[/tex]
Which is not correct. What did I do wrong?