Example(1):- A rope (AB) of length 35 m passing over a pulley of negligible sizeat (C) as shown in figure below, find the total time required to raise the mass of (B)from the ground to the point (C) if we know that the point (A) has a constantvelocity V 10 m/sec to the right.Solution:-BAT15msmV. 10 m/sec٤/٣ #Example(2):- A ball is dropped from rest at the top of a 60 m tower. A horizontalwind gives it a constant horizontal acceleration, and the ball hits the ground 3 meast of its release point. Neglect vertical air resistance and calculate the horizontalacceleration a, and the horizontal velocity V, of the ball as it hits the ground.Solution:-3mAT60m

Answered: Image /qna-images/answer/2e122193-1670-4db8-8fc7-ad0417f261d7.jpg

Answered: Example(1):- A rope (AB) of length 35 m…

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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QI) Two masses m, = 2 kg and m2 = 8 kg are attached to each other by a string passing through a massless pulley of radius R = 1m. m, is also attached to vertical spring of stiffness constant k = 20 N/m and equilibrium length 3h = 6m, while m2 is held at a height of h = 2m initially. If the system is released from rest, a) Find the speed of the blocks right before m2 hits the ground. m1 m2 3h h b) Repeat the question for the case where the pulley has a mass, hence a moment of inertia I = 30 kg · m².
FBD: The mass of a pendulum is connected to a spring with a spring constant Kas shown in the figure. The spring stays vertical all the time with the help of a massless follower. The vertical distance between the fixed point O and the path of the massless follower is 2L. Use Newton's second law and find the equation of motion of the system in terms of 0. 762 mgbi Img 2L L bil Nig K 777777 P EMO = Jaz ->0₂ ?
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A spring connects mass m of a pendulum to a wall as shown in the figure. The original un- stretched length of the spring is L. Use the Energy Method and find the equation of motion of the system in terms of the angle 0. L L K m Original Length = L
Suppose that you are designing a system to prevent the contents of packages from being damaged when they slide off of a conveyor line. Your solution is to have a linear spring that compresses 6 inches when a package weighing 80 pounds impacts the system at a speed of 10 feet per second. What value of k, the spring constant, should you specify? Assume that the spring is at its free length before the package makes contact, and that friction can be neglected. (Hint: remember to use consistent units!) 10 ft/s www. Problem 4: What is the maximum acceleration in g's that the package in the previous problem will experience? (Use equations of motion for this problem.)
A mechanical system consists of a ("long") rigid rod of length d and mass M, and another ("short") rigid rod of length I and mass m. The rods are attached at a fixed 90° angle such that the endpoint of the long rod touches the middle of the short rod; see the figure below. The mass per unit length of the rods is constant. The system can move in a vertical plane (x, y) with the endpoint O of the long rod fixed, so that the system is free to oscillate in the vertical plane about the point O. Gravity acts along the vertical y direction. 0 d a) How many degrees of freedom does the system have? [Expect to use a line to answer this question.] â b) Calculate the moment of inertia of the system constituted by the rods about an axis orthog- onal to the plane (x, y) and passing through O. Assume that the widths of the rods are negligible, so that you can effectively treat them as one-dimensional objects. [Expect to use about half a page to answer this question.] c) Determine the distance of the…
A beam is supported by a hinged joint at one end (O) and by a spring at the other end (A) as shown in the figure. The stiffness of the spring is such that the beam end A lies directly under the spring attachment point B when the spring is at its free length (no force). Using Hamilton's principle, develop the Euler-Lagrange equation of motion for the system when subjected to 1. A time-dependent vertical force applied at end A of the beam. 2. A time dependent force at end A of the beam that remains oriented perpendicular to the beam for all angles of the beam. Assume the following for your analysis 1. The beam is rigid. 2. The beam is uniform, i.e. its mass per unit length is constant) 3. The thickness of the beam is small compared to its length 4. The spring stiffness is constant. 5. The spring mass is small and can be ignored. 6. The angular displacements of the beam are not necessarily small. D F(t) F(t)
P.2) The lower link of the given mecha- nism is constrained to move horizontally with a velocity VA = 10i ft/s. At the depicted instant, A is located directly beneath the fixed pivot point C, and links AB and BC are orthogonal and of equal length, "B/A = 1.2 ft. Find w and VB. B/C A OB j
All this with steeps
full solution pls no short cut show the process
L W (1) (25pts) Find the description of the linear acceleration vector of the mass center of the segment (B) as functions of the distance (r), angular displacement (0), angular velocity (0), and angular acceleration (a). (2) (bonus: 5pts) Find the mass moment of inertia of the lower leg about the knee joint. Assume that the lower leg can be modeled as a cylinder. The length of the lower leg L is 30cm, and the diameter D is 4cm. The mass of the lower leg segment is 2kg. * This is a bonus problem - you learned how to calculate the mass moment of inertia in physics.
Example (3): A body moves on a straight line according to the equation: S = 4 t + 2 t2- 2 t + 5, where (s) is displacement, (t) is the time interva , Find out displacement, velocity , and acceleration when t= 3 sec . Solution: 2 12 - 2 t+ 5

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