Question

Question #a0c75

Answer 1

`a_("c") = 1008` `"m s"^(- 2)`

Explanation:

First, let's find the time period of this system.

The string fully rotates `25` times in `14` seconds.

Time period is defined as the time taken to complete one full rotation.

`Rightarrow "T" = frac(14 " s")(25)`

`therefore "T" = 0.56` `"s"`

The system is moving in a circular path, i.e. the acceleration is centripetal.

The equation for centripetal acceleration is `a_("c") = frac(v^(2))(r)`; where `a_("c")` is the centripetal acceleration, `v` is the velocity of the system, and `r` is its radius (in this case it's the length of the string, i.e. `8` `"m"`).

We still need to find the value of the velocity.

The equation for the velocity of an object travelling in a circular path is `v = frac(2 pi r)("T")`:

`Rightarrow v = frac(2 cdot pi cdot 8 " m")(0.56 " s")`

`therefore v = 89.8` `"m s"^(- 1)`

Now, let's find the centripetal acceleration:

`Rightarrow a_("c") = frac((89.8 " m s"^(- 1))^(2))(8 " m")`

`Rightarrow a_("c") = frac(8064 " m"^(2) " s"^(- 2))(8 " m")`

`therefore a_("c") = 1008` `"m s"^(- 2)`

Therefore, the acceleration of this system is `1008` `"m s"^(- 2)`.