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 :

Answer:

[tex]\frac{dF}{dr} = -4.82[/tex]

Explanation:

As we know that the centripetal force is given as

[tex]F = \frac{mv^2}{r}[/tex]

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

so we have

[tex]\frac{dF}{dr} = - \frac{mv^2}{r^2}[/tex]

so we have

m = 1000 kg

v = 13.89 m/s

r = 200 m

now we have

[tex]\frac{dF}{dr} = -\frac{1000(13.89^2)}{200^2}[/tex]

[tex]\frac{dF}{dr} = -4.82[/tex]

Kati19

Answer:

-4.823

Explanation:

rounded to the hundredth