A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the minimum speed required to keep the mass in circular motion?
Practice Questions
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Q1
A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the minimum speed required to keep the mass in circular motion?
√(g*r)
g*r
2g*r
g/2
At the highest point, the centripetal force is provided by the weight. Minimum speed = √(g*r).
Questions & Step-by-step Solutions
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Q
Q: A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the minimum speed required to keep the mass in circular motion?
Solution: At the highest point, the centripetal force is provided by the weight. Minimum speed = √(g*r).
Steps: 8
Step 1: Understand that when an object is whirled in a circle, it needs a force to keep it moving in that circle. This force is called centripetal force.
Step 2: At the highest point of the circle, the only force acting on the mass that can provide this centripetal force is its weight (the force due to gravity).
Step 3: The weight of the mass is calculated using the formula: Weight = m * g, where 'm' is the mass and 'g' is the acceleration due to gravity (approximately 9.81 m/s²).
Step 4: For the mass to stay in circular motion at the highest point, the centripetal force needed is given by the formula: Centripetal Force = (m * v²) / r, where 'v' is the speed and 'r' is the radius of the circle.
Step 5: At the minimum speed, the weight of the mass will equal the centripetal force required to keep it moving in a circle. So, we set the two forces equal: m * g = (m * v²) / r.
Step 6: We can simplify this equation by canceling 'm' from both sides (as long as m is not zero): g = v² / r.
Step 7: To find the minimum speed 'v', we rearrange the equation: v² = g * r.
Step 8: Finally, we take the square root of both sides to find the minimum speed: v = √(g * r).
