A stone with a mass of 0.800 is attached to one end of a string 0.800 long. The string will break if its tension exceeds 60.0 . 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
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To find the maximum speed the stone can attain without breaking the string, we need to consider the tension in the string when the stone is moving at its maximum speed.
In circular motion, the centripetal force is provided by the tension in the string. The centripetal force is given by the equation:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the stone
v is the velocity of the stone
r is the radius of the circular path
In this case, the tension in the string should not exceed 60.0 N. So we can set the maximum tension as an upper limit for the centripetal force:
T_max = F_max = (m * v_max^2) / r
Rearranging the equation, we can solve for v_max:
v_max = √((T_max * r) / m)
Now let's substitute the given values:
mass of the stone, m = 0.800 kg
length of the string, r = 0.800 m
maximum tension, T_max = 60.0 N
v_max = √((60.0 * 0.800) / 0.800)
v_max = √(48.00 / 0.800)
v_max = √60.00
v_max ≈ 7.75 m/s
The maximum speed the stone can attain without breaking the string is approximately 7.75 m/s.