Question

Notify Me Bookmark

A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 51.6 m. At the instant it makes an angle of 30.0∘ with the vertical as it falls, what are (a) the radial acceleration of the top, and (b) the tangential acceleration of the top. (Hint: Use energy considerations, not a torque.) (c) At what angle θ is the tangential acceleration equal to g? Assume free-fall acceleration to be equal to 9.81 m/s2.

A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 51.6 m. At the instant it makes an angle of 30.0∘ with the vertical as it falls, what are (a) the radial acceleration of the top, and (b) the tangential acceleration of the top. (Hint: Use energy considerations, not a torque.) (c) At what angle θ is the tangential acceleration equal to g? Assume free-fall acceleration to be equal to 9.81 m/s2.

Image text
A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 51.6 m . At the instant it makes an angle of 30.0 ∘ with the vertical as it falls, what are (a) the radial acceleration of the top, and (b) the tangential acceleration of the top. (Hint: Use energy considerations, not a torque.) (c) At what angle θ is the tangential acceleration equal to g ? Assume free-fall acceleration to be equal to 9.81 m / s 2 .

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

In a judo foot-sweep move, you sweep your opponent's left foot out from under him while pulling on his gi (uniform) toward that side. As a result, your opponent rotates around his right foot and onto the mat. The figure shows a simplified diagram of your opponent as you face him, with his left foot swept out. The rotational axis is through point O. The gravitational force F→g on him effectively acts at his center of mass, which is a horizontal distance d = 25 cm from point O. His mass is 84 kg, and his rotational inertia about point O is 65 kg⋅m2. What is the magnitude of his initial angular acceleration about point O if your pull F→a on his gi is (a) negligible and (b) horizontal with a magnitude of 300 N and applied at height h = 1.4 m? Assume free-fall acceleration to be equal to 9.81 m/s2. (a) Number Units (b) Number Units

Solution
0 0

A child of mass m is sitting at rest on a swing of length L. Their parent pulls them back making an angle of θ with the vertical as shown in the diagram. The parent uses a force that is perfectly horizontal. a) Find an expression for the force required to pull the child back as a function of the angle made by the swing. θ, m, L, and any fundamental can be in your answer. b) (Calculus version) i. Set up but do not solve an integral that could be used to calculate the work done on the child. ii. Now execute the integral showing that the work done will equal the resulting increase in potential energy. c) (Non calculus version) i. Find an expression for the height of the child above their lowest position as a function of θ and L. ii. Find an expression for the potential energy of the child in terms of m, θ, L, and any fundamental constants. d) The child is released and swings down to the lowest position. i. What is the tension in the cable the instant they are released? (Hint: their velocity the instant they are released is zero, but the net force is unbalanced. ) ii. What is the acceleration of the child the instant the parent releases them? iii. What is the speed of the child at the bottom of their swing? iv. What is the tension in the cable at the bottom of their swing?
Solution
0 0

The figure shows a thin rod, of length L = 1.30 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 8.60 kg is attached to the other end. The rod is pulled aside to angle θ0 = 17.0∘ and released with initial velocity v→0 = 0 . As the ball descends to its lowest point, (a) how much work does the gravitational force do on it and (b) what is the change in the gravitational potential energy of the ball-Earth system? (c) If the gravitational potential energy is taken to be zero at the lowest point, what is its value just as the ball is released?
Solution
0 0