In designing circular rides for amusement parks, mechanicalengineers must consid

Question

In designing circular rides for amusement parks, mechanicalengineers must consider how small variations in certain parameterscan alter the net force on a passenger. Consider a passenger ofmass m riding around a horizontal circle of radius r at speed v.What is the variation dF in the net force magnitude for thefollowing? (Use m, v, r, T, dr, dv, and dT as appropriate in yoursymbolic answers.)

(a) A variation dr in the radius with v held constant?
=(-mv^(2))/r^(2)*dr

(b) A variation dv in the speed with r held constant?
=(2mv)/r*dv

(c) A variation dT in the period with r held constant?
=????????????

HINT:(a) and (b) To find the variation in a quantity when aparameter changes, you take the derivative of the quantity withrespect to that parameter. (c) T depends on r and v. So, if Tvaries and r is held constant, v varies. You need to replace v inthe usual equation for the centripetal force, so that you can takea derivative with respect to T.

I just need help with finding C. well i know that T=2pi*r / (v)
and that F=mv^2/r so, i seem to be stumbling on this.

I got Dt= -{mv^3/pi*r2}dt which i thought was answer but it wasnt,any ideas?

Explanation / Answer

Hope this helps and you get full marks. Please rate me. a) dF/dr =(d/dr )(mv^2/r) = (-mv^2)/ r^2 b) dF/dv =( d/dv)/ (mv^2/r) =(2mv)/r c)v=(2r)/T F=(mv^2)/r F=(m/r) ((2r)/T)^2) F= (-8^2mr)/ T^3

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