Question

A string under a tension of 59.0 N is used to whirl a rock in a horizontal circle of radius 2.60 m at a speed of 20.3 m/s on a frictionless surface as shown in the figure below. As the string is pulled in, the speed of the rock increases. When the string is 1.00 m long and the speed of the rock is 49.5 m/s, the string breaks. What is the breaking strength, in newtons, of the string?

Answer 1

You can use the first set of info to find the mass of the rock, then use that and the centripetal acceleration of the second scenario to get the force.

Answer 2

please show me

Answer 3

Do you know how to find centripetal acceleration from linear speed and radius?

Answer 4

\[T=\frac{ mv^2 }{ r }\]

Answer 5

no

Answer 6

find the mass from here

Answer 7

.5 is the radius?

Answer 8

i need help dude

Answer 9

is it 59N * 20.3^2 all over 2.6

Answer 10

This is your initial info: "A string under a tension of 59.0 N is used to whirl a rock in a horizontal circle of radius 2.60 m at a speed of 20.3 m/s"
T=59.0N, r=2.60m, v=20.3m/s.
You can use the formula provided by Yahoo! to find mass, m.

Answer 11

so i did it right, now i need m ?

Answer 12

No, you multiplied force by the square of the velocity. If you divide that by 2.6m then you'll get units of kg*m^2/s^4 which is non-physical.

Answer 13

so i got little m to be .3722987806

Answer 14

Always include the units in your calculations, they'll make sure you keep things in the proper dimension.

Answer 15

so once i have little m, now what? i mean i hope its correct

Answer 16

Yes, m=0.372kg.
Now find the centripetal acceleration in the second scenario and multiply by the mass to get the new force.

Answer 17

i just did .372*49.5 = 18.42

Answer 18

is that right?

Answer 19

Don't forget to square the velocity to get acceleration.

Answer 20

so square 49.5

Answer 21

Again, watch your units:
\[\frac{v^2}{r}=\frac{[m/s]^2}{[m]} = \frac{[m]}{[s]^2} = acceleration.\]

Answer 22

a Ferris wheel that rotates five times each minute. It carries each car around a circle of diameter 18.0 m. What force (magnitude and direction) does the seat exert on a 53.0-kg child when the rider is halfway between top and bottom?

Answer 23

Taking a look at it now...