Consider a stationary inclined plane ramp with a fixed angle 6, with three blocks with equal...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a stationary inclined plane ramp with a fixed angle 6, with three blocks with equal masses M attached by a spring of constant k and a string over a fixed pulley at the top of the ramp, as shown below. The positions of the blocks are described by the distances r(t) (the distance from the pulley to the higher block on the ramp) and y(t) (the extension of the spring), as shown. The system is in a uniform graviational field of acceleration g. The unstretched length of the spring is 0, and the pulley is massless. 0000000 (a) [12 points] Find the Lagrangian and the equations of motion of the system. (b) [20 points] The two blocks on the ramp are released from rest at the top with a = y = 0 at time t = 0. Find the motions of the blocks as a function of time. %3D (c) [8 points] The choice 0 = 30 degrees has a special significance, which should be apparent in the results of part (b). What is it? Consider a stationary inclined plane ramp with a fixed angle 6, with three blocks with equal masses M attached by a spring of constant k and a string over a fixed pulley at the top of the ramp, as shown below. The positions of the blocks are described by the distances r(t) (the distance from the pulley to the higher block on the ramp) and y(t) (the extension of the spring), as shown. The system is in a uniform graviational field of acceleration g. The unstretched length of the spring is 0, and the pulley is massless. 0000000 (a) [12 points] Find the Lagrangian and the equations of motion of the system. (b) [20 points] The two blocks on the ramp are released from rest at the top with a = y = 0 at time t = 0. Find the motions of the blocks as a function of time. %3D (c) [8 points] The choice 0 = 30 degrees has a special significance, which should be apparent in the results of part (b). What is it?
Expert Answer:
Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
Posted Date:
Students also viewed these mechanical engineering questions
-
A 2-kg block is supported by a spring of constant k = 128 N/m and a dashpot with a coefficient of viscous damping c = 0.6 N ?? s/m. The block is in equilibrium when it is struck from below by a...
-
A light spring of constant k = 90.0 N/m is attached vertically to a table (Fig. P14.59a). A 2.00-g balloon is filled with helium (density = 0.180 kg/m3) to a volume of 5.00 m3 and is then connected...
-
Two bars are attached to a single spring of constant k that is unstretched when the bars are vertical. Determine the range of values of P for which the equilibrium of the system is stable in the...
-
Two 20-in. rods AB and DE are connected as shown. Point D is the midpoint of rod AB, and at the instant shown rod DE is horizontal. Knowing that the velocity of point A is 1 ft/s downward, determine...
-
The Excel file Credit Approval Decisions provides information on credit history for a sample of banking customers. Use regression analysis to identify the best model for predicting the credit score...
-
A transport company has 4 trucks of the same type. There are 2 maintenance teams for repairing the trucks after a failure. Each team can repair only one truck at a time and each failed truck is...
-
1. Which normal curve has a greater mean? 2. Which normal curve has a greater standard deviation?
-
Should Charlies strategy include direct response or confrontation with the negative poster identified by Burris? Look at this! What should we do about it? exclaimed Seymour Burris, Jr., the President...
-
b) Explain what decision-making is (no more than 50 words for each) i) according to the legal context of Anishinaabe nations ii) according to the context of CPA professional standards quoted from...
-
Diana and Ryan Workman were married on January 1 of last year. Diana has an eight-year-old son, Jorge, from her previous marriage. Ryan works as a computer programmer at Datafile Inc. (DI) earning a...
-
0 A dispatcher is working on the truck route for tomorrow's deliveries. Given that he uses the nearest neighborhood search. a. Calculate potential routes (i.e. if there are ties you need to branch...
-
Describe the effects of this transaction on the accounting equation in terms of debits and credits. The new equipment was purchased for 6 4 2 3 6 on January 1 st . As of that date, the property,...
-
describe the linkage between performance management outcomes and broader organizational outcomes such as productivity, profitability, and employee engagement?
-
Describe the different issues related to environmental scanning, strategy formulation, and strategy implementation in diversified organizations (CLO2) Distinguish between different types and levels...
-
Describe a cognitive bias that may skew an entrepreneur's perception of the opportunity to open a new hip - hop dance studio near Ryerson's campus. Why is an entrepreneur more prone to this bias...
-
Consider a production process where flowers are grown (the output) using gardeners (labor) and greenhouses (capital). The quantity of flowers grown per day with various combinations of labor and...
-
A risk defined as "a Campylobacter risk of 1 per million" is well defined.
-
Suppose the index goes to 18 percent in year 5. What is the effective cost of the unrestricted ARM?
-
A homogeneous wire with a mass per unit length of 1.8 kg/m is used to form the figure shown. Determine the mass products of inertia Ixy, Iyz, and Izx of the wire figure. 0.5 m 0S m OS m
-
Knowing that the line of action of the force Q passes through point C, derive an expression for the magnitude of Q required to maintain equilibrium. A B 2- D E
-
Solve Prob. 7.94 assuming that dC = 9 ft. Problem 7.94: An oil pipeline is supported at 6-ft intervals by vertical hangers attached to the cable shown. Due to the combined weight of the pipe and its...
-
What orientation of an electric dipole in a uniform electric field has the greatest electric potential energy? What orientation has the least? (Let the system comprise both the electric dipole and...
-
You release three balls simultaneously from the same height above the floor. The balls all carry the same quantity of surplus positive charge, but they have different masses: \(1 \mathrm{~kg}, 2...
-
A dipole carrying charges \(+q\) and \(-q\) separated by a distance \(d\) is rotated \(180^{\circ}\) in a uniform electric field (Figure P25.7). What is the change in electric potential energy...
Study smarter with the SolutionInn App