Question #5752

when you have a rock on a string spinning it around, if you have a original tension with a radius and velocity, how would you find the breaking strength of a string if the problem also states a second radius and velocity but not the tension?

Expert's answer

Let's make the following denominations:

F1 - the original tension

R1 = original radius

V1 = original velocity

R2 = second radius

V2 = second velocity

M - the mass of a rock

We need to find the mass of a rock at first.

Using the first case we have that the centripetal acceleration of a rock is

Ac1 = V1²/R1.

Now let's use the second Newton's law:

F1 = M*Ac1 ==> M = F1/Ac1 = F1/(V1²/R1) = F1*R1/V1².

Now let's find the breaking strength of the string.

In the second case we have that the centripetal acceleration of a rock is

Ac2 = V2²/R2.

So, we can find the breaking strength usind the second Newton's law again:

F2 = M*Ac2 = (F1*R1/V1²)*(V2²/R2) = (F1*R1*V2²)/(V1²*R2).

F1 - the original tension

R1 = original radius

V1 = original velocity

R2 = second radius

V2 = second velocity

M - the mass of a rock

We need to find the mass of a rock at first.

Using the first case we have that the centripetal acceleration of a rock is

Ac1 = V1²/R1.

Now let's use the second Newton's law:

F1 = M*Ac1 ==> M = F1/Ac1 = F1/(V1²/R1) = F1*R1/V1².

Now let's find the breaking strength of the string.

In the second case we have that the centripetal acceleration of a rock is

Ac2 = V2²/R2.

So, we can find the breaking strength usind the second Newton's law again:

F2 = M*Ac2 = (F1*R1/V1²)*(V2²/R2) = (F1*R1*V2²)/(V1²*R2).

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