Answered: Ultimate goal: Determine the angular…

Engineering

Mechanical Engineering

Ultimate goal: Determine the angular velocity of the pendulum when it rotates clockwise 90 degrees.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question 2: The ideal spring of constant k-2.6 kN/m is attached to the disk at point A and the end fitting at point B, as shown. The spring is unstretched when OA and Oв are both zero. If the disk is rotated 15° clockwise and the end fitting is rotated 30°counterclockwise, determine the vector expression for the spring force F. ( Determine distance C so that the moment the spring force makes about the Z axis is equal to 10.82 N.m. ( A = 15°. C A 250 mm eeeeeee 900 mm k= 2.6 kN/m OB = 30° B LC 7-y 200 mm
1. In lecture I focused on a horizontal mass-spring system so we could ignore gravity, but in practice it's much easier to build a vertical mass-spring system. In the figure below, we can see a suspended spring with spring constant k both before and after a mass m is hooked to it. Y Yo yo is the equilibrium height of the spring (without the mass) and in the figure y = 0 is set at the ground. a) Using the coordinate system in the figure, show that Newton's second law for the hanging mass-spring system leads to the following differential equation: d²y dt² k (y - Yo) - g m b) Now define a new coordinate, y', related to y by a constant shift: y = y' + C, where C = constant. Show that if you choose the right value of C, Newton's second law is identical in form to a mass-spring system without gravity. What is the period of the system? c) Effectively, gravity just shifts the equilibrium position of the system, but the system still undergoes simple harmonic motion. What is the net force on the…
The 4.00 kg block is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the (Figure 1) and the tension in the upper string is 84.0 N. (A) What is the tension in the lower cord? (Express your answer with the appropriate units.) (B) How many revolutions per minute does the system make? (Express your answer in revolutions per minute.) (C) Find the number of revolutions per minute at which the lower cord just goes slack. (Express your answer in revolutions per minute.)
Question 2: The ideal spring of constant k-2.6 kN/m is attached to the disk at point A and the end fitting at point B, as shown. The spring is unstretched when OA and Oв are both zero. If the disk is rotated 15° clockwise and the end fitting is rotated 30°counterclockwise, determine the vector expression for the spring force F. Determine distance C so that the moment the spring force makes about the Z axis is equal to 10.82 N.m. - A = 15°1 A 250 mm lllllll 900 mm k = 2.6 kN/m OB = 30° B G 200 mm
2. A 4-lb weight stretches a spring 6 in. The weight is pulled 3 in below the equilibrium position and released. Find the motion of the weight if an cos6t acts on the system. external force f(x) = 4 F(x)= Ma -what is the spring constan" K-F 4 7=33
I Draw the free-body diagrams and write the differential equations of motion for the two masses in terms of x₁ and .x2. b. Find x₁, and X20, the constant displacements of the masses caused by the gravita- tional forces when fa(t) = 0 and when the system is in static equilibrium. K₁ Rewrite the system equations in terms of z₁ and 22, the relative displacements of the masses with respect to the static-equilibrium positions found in part (b). K₂ ele M₂ fa(1) M₁ IIL B Figure P2.15 111 ele /// K M₁ 000 M₂ K ( 000 K fa(1) Figure P2.16 2.16. Repeat all three parts of Problem 2.15 for the system shown in Figure P2.16. Each of the three springs has the same spring constant K.
Three masses are attached to a uniform meter stick, as shown in figure. The mass of the meter stick is 150.0 g and the masses to the left of the fulcrum are m1 = 50 kg, m2 = 75 kg, and m3 that balances the system when it is attached at the right end of the sticky, and the normal reaction force at the fulcrum when the system is balanced. Also, find the mass m3.
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The linkage shown is used in a vehicle suspension system. Find the forces indicated below when a static force of F = 1000 lb is applied to the tire at point C at an angle of 0 = 17° as shown. Assume the connection of the wheel to member AB is rigid. 1 h₁ K: LOFF 0 W₁ h₂ h3 h4 h5 B W₁₂ AXHIMAL W4 hs: h₂ cc i❀O BY NC SA 2013 Michael Swanbom W3 - W₁ Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value Variable Value h₁ 6.6 in W1 7.5 in 16.6 in W2 4.6 in 14.6 in W3 8.3 in 10.2 in W4 6.2 in 5.2 in W5 9.7 in