Question

Find A mass of 10 kg is moving in a circular path of radius 2 m with a uniform speed of 50 ms the centripetal acceleration and the corresponding centripetal force​

Answer 1

Centripetal acceleration:
`1250\; {\rm m\cdot s^(-2)}`.

Resultant force on the object should be
`12500\; {\rm N}`.

(Assuming that the speed of the object is
`50\; {\rm m\cdot s^(-1)}`.)

Step-by-step explanation:

For an object that travels along a circle path of radius
`r` at a speed of
`v`, (centripetal) acceleration will be
`a = (v^(2) / r)`.

In this example, speed is
`v = 50\; {\rm m\cdot s^(-1)}` while the radius of the circular path is
`r = 2\; {\rm m}`. The (centripetal) acceleration of this object will be:

`\begin{aligned}a &= (v^(2))/(r) \\ &= \frac{(50\; {\rm m\cdot s^(-1)})^(2)}{(2\; {\rm m})} \\ &= 1250\; {\rm m\cdot s^(-2)}\end{aligned}`.

For an object of mass
`m`, the resultant force to achieve acceleration
`a` is
`F(\text{net}) = m\, a`. In this example,
`m = 10\; {\rm kg}` while
`a = 1250\; {\rm m\cdot s^(-2)}`. The required resultant force will be:

`\begin{aligned}F(\text{net}) &= m\, a \\ &= (10\; {\rm kg})\, (1250\; {\rm m\cdot s^(-2)}) \\ &= 12500\; {\rm kg \cdot m\cdot s^(-2)} \\ &= 12500\; {\rm N} \end{aligned}`.