Question

The centripetal force of an object of mass m is given by F(r)=mv2r, where v is the speed of rotation and r is the distance from the center of rotation. Find the rate of change of centripetal force with respect to r of an object with mass 1000 kilograms, velocity of 13.89m/s and a distance from the center of rotation of 200 meters. Do not include units in your answer, and round to the nearest thousandt

Answer 1

Answer:

$\frac{dF}{dr} = -4.82$

Explanation:

As we know that the centripetal force is given as

$F = \frac{mv^2}{r}$

now we will have to find the rate of change in force with respect to its radial distance

so we have

$\frac{dF}{dr} = - \frac{mv^2}{r^2}$

so we have

m = 1000 kg

v = 13.89 m/s

r = 200 m

now we have

$\frac{dF}{dr} = -\frac{1000(13.89^2)}{200^2}$

$\frac{dF}{dr} = -4.82$