Question

A dog sits 1.70 m from the center of a merrygo-round with an angular speed of 1.27 rad/s. If the magnitude of the force that maintains the dog’s circular motion is 40.3 N, what is the dog’s mass? Answer in units of kg.

Answer 1

Answer : The mass of dog is, 14.7 kg

Solution :

Formula used for centripetal force is,

$F_c=\frac{m\times v^2}{r}$

As we know that,

$\omega =\frac{v}{r}$

or,

$\omega \times r=v$

So,

$F_c=\frac{m\times (\omega \times r)^2}{r}$

$F_c=m\times (\omega)^2\times r$

where,

$F_c$ = centripetal force  = 40.3 N

m = mass of dog = ?

r = radius of path  = 1.70 m

v = velocity or speed

$\omega$ = angular speed = 1.27 rad/s

Now put all the given values in the above formula, we get the centripetal force.

$F_c=m\times (\omega)^2\times r$

$40.3=m\times (1.27)^2\times (1.70)$

$m=14.7kg$

Thus, the mass of dog is, 14.7 kg