A pendulum string of length 
is moves up to a horizontal position (fig.) and released. What should the minimum strength of the string be to withstand the tension as the pendulum passes through the position of equilibrium? The mass of the pendulum is m.
Text Solution
Verified by ExpertsA
The pendulum passes through the equilibrium position moving along the arc of a circle of radius
with a velocity v . At this moment the bob of the pendulum will possess a centripetal acceleration a = 
directed upwards. This acceleration is provided by the joint action of the force of gravity and the tension in the thread (fig.).
By Newton's second law,
F – mg = m 
and hence F = m 
The velocity v is determined from the law of conservation of energy and is
v = 
and therefore F = mg + 
= 3 mg = 3P
where P is the weight of the bob. The thread must be able to support a load equal to three times the weight of the bob.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems