Question

A stone with a mass of 0.700kg is attached to one end of a string 0.600m long. The string will break if its tension exceeds 65.0N . The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed.
Find the maximum speed the stone can attain without breaking the string? m/s

Answer 1

Answer:v=7.46 m/s

Explanation:

Given

mass of stone=0.7 kg

Length of string=0.6 m

Maximum tension in string T=65 N

Tension will Provide centripetal force i.e. $\frac{mv^2}{r}$

$T=\frac{mv^2}{r}$

$65=\frac{0.7\times v^2}{0.6}$

$65\times 0.6=0.7\times v^2$

$v^2=\frac{65\times 0.6}{0.7}$

$v^2=55.71$

$v=\sqrt{55.71}=7.46 m/s$

Answer 2

The maximum speed that the stone can attain without breaking the string is  7.46 m/s.

How to calculate maximum velocity from Tension?

The tension of the string is equal to the centripetal force. It can be represented as,

$T = F_c$

$T = \dfrac {mv^2}{R}$

Where,

$T$ - tension = 65 N

$m$ - mass  = 0.7 g

$v$ -velocity = ?

$R$ - Radius = 0.6 m

Put the values in the formula and calculate for $v$,

$65 = \dfrac {0.7 \times v^2}{0.6}$

$v = \sqrt {65\times 0.6}{0.7}$

$v = 7.46 \rm \ m/s$

Therefore, the maximum speed that the stone can attain without breaking the string is  7.46 m/s.

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