A mass m is attached to a string and is whirled in a vertical circle. At the hig
Practice Questions
Q1
A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
T = mg
T = mg - mv²/r
T = mg + mv²/r
T = mv²/r
Questions & Step-by-Step Solutions
A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
Step 1: Understand that the mass m is moving in a vertical circle and at the highest point, there are two forces acting on it: the tension in the string (T) and the weight of the mass (mg).
Step 2: Recognize that at the highest point, both the tension (T) and the weight (mg) contribute to the centripetal force needed to keep the mass moving in a circle.
Step 3: Write down the equation for centripetal force at the highest point: T + mg = mv²/r, where v is the speed of the mass and r is the radius of the circle.
Step 4: Rearrange the equation to solve for the tension (T). Start with T + mg = mv²/r.
Step 5: Subtract mg from both sides to isolate T: T = mv²/r - mg.
Step 6: Factor out m from the right side: T = m(v²/r - g).
Step 7: This gives you the expression for the tension T at the highest point of the circle.
Centripetal Force – The net force acting on an object moving in a circular path, which is required to keep the object moving in that path.
Forces in Circular Motion – Understanding how gravitational force and tension interact at different points in a vertical circular motion.
Newton's Second Law – The relationship between the forces acting on an object and its motion, particularly in circular motion.
