Question

Notify Me Bookmark

A simple pendulum is pivoted at O and is free to swing in the vertical plane of the plate. If the plate is given a constant acceleration a = 4.6 m/s2 up the incline θ = 24∘, find the steady angle β assumed by the pendulum after all initial start-up oscillations have ceased. Neglect the mass of the slender supporting rod. Answer: β =

A simple pendulum is pivoted at O and is free to swing in the vertical plane of the plate. If the plate is given a constant acceleration a = 4.6 m/s2 up the incline θ = 24∘, find the steady angle β assumed by the pendulum after all initial start-up oscillations have ceased. Neglect the mass of the slender supporting rod. Answer: β =

Image text
A simple pendulum is pivoted at O and is free to swing in the vertical plane of the plate. If the plate is given a constant acceleration a = 4.6 m / s 2 up the incline θ = 24 ∘ , find the steady angle β assumed by the pendulum after all initial start-up oscillations have ceased. Neglect the mass of the slender supporting rod.
Answer: β = ◻

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

A ring of mass m slides over a rod with mass M and length L, which is pivoted at one end and hangs vertically. The mass m is secured to the pivot point by a massless spring of spring constant k and unstressed length l. For θ = 0 and at equilibrium m is centered on the rod. Consider motion in a single vertical plane under the influence of gravity. 1. Show that the potential energy is V = k/2(r - L/2)^2 + mgr( 1 - cosθ) – 1/2MgLcosθ. 2. Write the system Lagrangian in terms of r and θ. 3. Obtain the differential equations of motion for r and θ. 4. In the limit of small oscillations find the normal mode frequencies. To what physical motions do these frequencies correspond?
Solution
0 0

The crate shown in Figure Q1.2 has a mass of m kg and is being raised up a plane at θ degrees by cable parallel to the plane. The coefficient of friction is μ. FIGURE 1.2 Note that values for m, θ and μ are randomly generated. Calculate the magnitude of the tension, T, that will allow an acceleration of a m/s2 up the plane. Note: the value for a is randomly generated. Given that the mass is initially at rest, what is its velocity after it has moved a distance of s m along the plane? Assume that the mass remains on the incline during this motion. Note: the value for s is randomly generated. Note also: constant acceleration can be assumed. What is the work done after the mass has moved a distance of s m?

Solution
0 0

In the diagram shown, Block A is 34.5 kg and Block B is 11 kg. The incline on Block A's side makes an angle of 61.5∘ with the horizontal and the incline on Block B's side makes an angle of 29∘ with the horizontal. The coefficient of kinetic friction of Block A's incline is 0.16 and that of Block B's incline is 0.104 . Assume that Block A is initially (at t = 0) sliding up its incline at 5.2 m/s. Also assume the pulley is massless and frictionless. In your submitted work, be sure to show your neatly drawn free body diagrams for each mass (using a straight-edge). Identify each vector force (draw arrows) in the diagram and draw your axes for each diagram and show the component breakdown for each force. . . points will be lost for sloppy or incomplete drawings. You should have FOUR FBDs. . . one for each mass as Block A slides UP the incline (while Block B slides DOWN its incline), and one for each mass when Block A slides DOWN its incline (while Block B slides UP its incline). (A)Calculate the magnitude of the acceleration (in m/s2) of the blocks as Block A is on the way UP its incline. 20.1 5.36 2.40 9.25 6.16 13.0 (B)Calculate the tension (in N) in the rope as Block A is on the way UP its incline. 233 95.9 43.0 110. 359 165 (C)Calculate the magnitude of the acceleration (in m/s2)of the blocks as Block A is on the way DOWN its incline. 15.0 9.70 1.79 4.60 4.00 6.90 (D)Calculate the tension (in N) in the rope as Block A is on the way DOWN its incline. 367 238 98.0 43.9 113 169 (E)Assuming the ramps and ropes are long enough, over what total distance (in meters) will the blocks have moved along their inclines after 3.5 seconds from start of the motion? (HINT: This is asking for distance, not displacement. ALSO, recognize that at some point over this 3.5 second time interval the blocks will stop and reverse direction.) 27.6 18.4 38.9 7.18 16.0 60.0
Solution
0 0