Question

A sling is being rotated at the rate of 100 rpm

a) What will the length of the sling have to be so that the speed of the object

at the end will be 40 meters per second? (in meters)

b)

If the sling is 1 meter long, how fast will the object at the end be

traveling? (in meters per second)

How many revolutions will the sling make over one hour?

Answer 1

a)
`r = 3.820\,m`, b)
`v\approx 10.472\,(m)/(s)`

Step-by-step explanation:

a) The needed length is found by the following formula:

`r = (v)/(\omega)`

`r = (40\,(m)/(s) )/((100\,rpm)\cdot((2\cdot \pi)/(1\,rev) )\cdot ((1\,min)/(60\,s) ))`

`r \approx 3.820\,m`

b) The required speed is:

`v = \omega \cdot r`

`v = (100\,rpm)\cdot ((2\cdot \pi)/(1\,rev) )\cdot ((1\,min)/(60\,s) )\cdot(1\,m)`

`v\approx 10.472\,(m)/(s)`