a stone with a mass of .700kg is attached to the end of a rting 0.900m long. the string will break if its tension exceed 60.0 N. the stone is whirled in a horizontal circle on a frictionless tabletop; the other of the string remain fixed. Find the maximum speed the stone can attain without breaking the string?
60N=.7*V^2/.9
solve for V
To find the maximum speed the stone can attain without breaking the string, we can consider the tension force in the string.
The tension force in the string is given by the centripetal force required to keep the stone in circular motion:
Fc = Tension = mass × centripetal acceleration
The centripetal acceleration is given by:
ac = v^2 / r
where v is the velocity of the stone and r is the radius of the circular motion.
Since the stone is whirled in a horizontal circle, the tension force is equal to the weight of the stone:
Tension = Weight = mass × gravitational acceleration
Substituting the centripetal acceleration expression into the tension equation, we get:
mass × v^2 / r = mass × gravitational acceleration
Canceling out the mass on both sides of the equation, we have:
v^2 / r = gravitational acceleration
Solving for v, we get:
v = √(r × gravitational acceleration)
Now we can substitute the given values:
r = 0.900 m
gravitational acceleration = 9.8 m/s^2
Plugging in these values, we get:
v = √(0.900 × 9.8)
Calculating that expression, we find:
v ≈ 3.04 m/s
Therefore, the maximum speed the stone can attain without breaking the string is approximately 3.04 m/s.
To find the maximum speed that the stone can attain without breaking the string, we need to consider the forces acting on the stone. The tension in the string must be less than or equal to 60.0 N for it not to break.
When the stone is whirled in a horizontal circle, the two main forces acting on it are the tension force in the string and the centripetal force required to keep the stone moving in a circle.
The centripetal force is given by the equation:
Fc = (mv^2) / r
Where Fc is the centripetal force, m is the mass of the stone, v is its velocity, and r is the radius of the circle (in this case, the length of the string).
In this problem, we need to find the maximum velocity v that the stone can have without exceeding the tension limit of 60.0 N.
To solve for v, we rearrange the equation:
v^2 = (Fc * r) / m
The maximum tension force is equal to the maximum tension the string can handle, which is 60.0 N.
So, plugging in the values:
v^2 = (60.0 N * 0.900 m) / 0.700 kg
v^2 = 77.14 m^2/s^2
Taking the square root of both sides of the equation:
v = √(77.14 m^2/s^2)
v ≈ 8.79 m/s
Therefore, the maximum speed the stone can attain without breaking the string is approximately 8.79 m/s.