A stone of mass 0.29 kg is tied to a string of length 0.55 m and is swung in a horizontal circle with speed v. The string has a breaking-point force of 85 N. What is the largest value v can have without the string breaking?
To determine the largest value of v without the string breaking, we need to consider the centripetal force acting on the stone when it is swung in a horizontal circle. The centripetal force is provided by the tension in the string.
The centripetal force (Fc) can be calculated using the formula:
Fc = (m * v^2) / r
Where:
m = mass of the stone (0.29 kg)
v = speed of the stone
r = radius of the circle formed by the string (length of the string, 0.55 m)
In this case, the breaking-point force of the string (Fb) is given as 85 N. Therefore, the tension in the string must be less than or equal to the breaking-point force (T ≤ Fb) to avoid breaking.
Therefore, we equate the centripetal force to the breaking-point force:
(m * v^2) / r = Fb
Rearranging the equation, we can solve for v:
v = √((Fb * r) / m)
Plugging in the given values, we have:
v = √((85 N * 0.55 m) / 0.29 kg)
Calculating the value, we find:
v ≈ 7.94 m/s
Therefore, the largest value v can have without the string breaking is approximately 7.94 m/s.