Question

Determine the magnitude of a ball's radial acceleration?

I'd appreciate a sketch too, since I'm not sure if mine is correct.

Answer 1

All answers rounded to one decimal place.

Explanation:

(a) As above.
(b) Total acceleration `veca` is given as `(-22.5hati+20.2hatj) " ms"^-2`
We know that

`veca=veca_t+veca_r`
where `veca_t and veca_r` are tangential and radial accelerations respectively.

From the figure
Total acceleration `veca` has its components along `x andy`-axes. Calculate component of each along the radius indicated by the rope. Sum of these gives us `|veca_r|`
`:.|veca_r| = 22.5 cos53.1^@ + 20.2cos36.9^@ =13.51+16.15= 29.7" ms"^-2`
(c) For circular motion we know that

`a_r = v^2 / r`
where `v` is velocity and `r` is radius of circle in which movement occurs

Inserting given and calculated values we get

`29.7 = v^2 / 1.5`
`=> |vecv|= sqrt(29.7 xx1.5)=6.7" ms"^-1`

Since velocity is tangential it makes and angle `=36.9^@` with the horizontal. Therefore, its components along the `xand y` axes are

`vecv=6.7cos36.9 hati + 6.7 sin36.9 hatj`
`vecv=(5.4 hati + 4.0 hatj)" ms"^-1`