Question

What is the fastest the block can be spun at without breaking with the block weighing 10kg and spinning horizontally with a 2m string. The string can hold 450 N of tension before breaking

Answer 1

The fastest speed before the string breaks is 9.5 m/s

Explanation:

The motion of the block is a uniform circular motion, which is a circular motion with constant speed. The force that keeps the block in circular motion is called centripetal force; its direction is towards the centre of the circle and its magnitude is given by:

$F=m\frac{v^2}{r}$

where

m is the mass of the block

v is its speed

r is the radius of the circle

In this problem, the centripetal force is provided by the tension in the string, T, so we can write:

$T=m\frac{v^2}{r}$

The string breaks when the centripetal force becomes larger than the maximum tension in the string:

$T_{max}<m\frac{v^2}{r}$

Re-arranging the equation  for v,

$v>\sqrt{\frac{Tr}{m}}$

and here we have:

T = 450 N

m = 10 kg

r = 2 m

Substituting,

$v>\sqrt{\frac{(450)(2)}{10}}=9.5 m/s$

So, the fastest speed before the string breaks is 9.5 m/s.

Learn more about circular motion:

brainly.com/question/2562955

brainly.com/question/6372960

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