4 ProblemConsider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. Theslider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of theslider is v, and the spring is stretched to length r>lo, where lo is its unstretched length. Thespring forms an angle 0 as shown and the spring constant k is unknown. If, at the instant shown,0 = 0 and r = 0 in the polar frame then what must the spring constant be? Also determine thenormal force at this instant. Express both in terms of one or more of the following variables:(v, m,r,lo,0). (Hint: first solve for r and from the velocity kinematics.)Motion in horizontal planePV

Given data:No radial acceleration, No angular acceleration,

Consider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is v, and the spring is stretched to length r > lo, where lo is its unstretched length. The spring forms an angle as shown and the spring constant k is unknown. If, at the instant shown, 0 = 0 and i = 0 in the polar frame then what must the spring constant be? Also determine the normal force at this instant. Express both in terms of one or more of the following variables: (v, m,r,lo,0). (Hint: first solve for r and è from the velocity kinematics.)

Consider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. The slider moves in the horizontal plane (there is no gravity). At the instant shown, the speed of the slider is v, and the spring is stretched to length r > lo, where lo is its unstretched length. The spring forms an angle as shown and the spring constant k is unknown. If, at the instant shown, 0 = 0 and i = 0 in the polar frame then what must the spring constant be? Also determine the normal force at this instant. Express both in terms of one or more of the following variables: (v, m,r,lo,0). (Hint: first solve for r and è from the velocity kinematics.)

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

See similar textbooks

Similar questions

2. A kilogram mass is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (a) Write the initial-value problem which describes the position of the mass. (b) Find the solution to your initial-value problem from part (a). (c) Graph the solution found in (b) on (0
3. Quarter car suspension model The figure below a model of the suspension of a car. r(t)is the position of the mass of the car from its equilibrium position while z is the profile of the road. Note that z is a function of the distance y along the road, but you need ż(t) which you can obtain from z(y) using the chain rule. The car is traveling to the right on the road at a speed v. Assume the mass of the car is 250 kg, the spring constant is 16 kN/m, and damping constant is 1000 Ns/m. (a) Derive the differential equation for the position of the car r(t). (b) If z(t) = Zoejot, determine the amplitude and the phase of the particular solution. (c) (MATLAB) If the car is travelling with constant velocity along a road with rolling hills that can be represented as a cosine function with amplitude Zo and wavelength A (wavelength is the distance between adjacent crests or adjacent troughs, determine the vertical motion of the car as a function of time. X(t) Z m 1 C Figure 1: Quarter car…
• View Available Hint(s) Learning Goal: To set up and analyze equations of motion in a cylindrical coordinate system. A = 4.30 rad/s Submit Previous Answers The mechanism shown in the figure below rotates about the vertical axis. The collar has mass an unstretched length of 1000 mm and the spring constant is k = 220 N/m. The distance d= 385 mm , and the collar is required to stay a fixed distancer = 1320 mm from the vertical axis.(Figure 1) = 3.25 kg. The spring has v Correct Part B- The minimum required angular velocity when there is friction Consider the same mechanism again, with m = 3.25 kg, d = 385 mm, k = 220 N/m, only now, instead of being smooth, the collar and shaft have a maxirmurm coefficient of friction of p. = 1.36. What is the minimum angular velocity required to keep the collar at a constant distance r= 1320 mm from the axis of rotation? Express your answer to three significant figures. Figure 1 of 1> • View Available Hint(s) η ΑΣφ It vec rad/s Submit d Part C Complete…
1. A weight of 8 lbf is attached to the end of a vertical spring which stretches 4 inches before reaching equilibrium. If the weight is pulled down 6 inches below equilibrium point and given an initial upward velocity of 8 ft/sec, find the equation of motion. Note: In solving for the spring constant k, make sure it ends up as a positive number.
Problem Statement: A car drives on a circular track with radius 270 m. Initially, the displacement s=0 and the speed is 24 m/s. The car then begins to accelerate at At 0.3s (given in m/s? where s is in meters). After 3.4 seconds has passed, determine: (To get this answer you may need to use a table of integrals and/or a numerical equation solver.) The distance traveled: ûn The velocity vector: un The acceleration vector: Be sure to include units with your answers.
A four-bar mechanism is used to transmit power to slider E. Link AC rotates counterclockwise at 100 rpm. A and B are fixed points. The following linkages are measured in cm: AC=35, AB=70, CD=45, BD=45, DE=40. Find the instantaneous velocity of slider E in cm/s 1.Draw the mechanism in appropriate scale on your paper2. Find the instantaneous linear velocity of C3. Find a point on your paper to draw the velocity polygon and scale the magnitude of the computed linearvelocity4. Use the relative velocity equation for finding the linearvelocity of D; ? = ? + ?? ? ?/?5. Remember that although the magnitudes are unknown, their directions can be identified6. Obtain the magnitudes of the unknown velocities from the velocity polygon7. For Link DE, repeat the process by using ? = ? + ??the line as much as needed8. Remember that E is a SLIDER therefore it can only goin the direction where its movement is not constrained? . Add the vector ? to the head of ? and extend?/? ?/??
Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 29 h by exerting a force parallel to the equator, opposing the rotation. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.15 × 107 N. For the purposes calculations in this problem you should treat the Earth as a sphere of uniform density even though it isn't. a. How long, in seconds, must Zorch push with this force to accomplish his goal? (This period gives Superman time to devote to other villains.)
Q3. (a) In Figure Q3 (a), a 27 gram bullet with velocity of 395 m/s is fired to the block in rest condition. Calculate the velocity of bullet and block when the bullet is embedded in the block after the impact. Use your matrix number to get the value of block mass (kg) as in example. Example: If your matrix number is AD190005, use the 4 numbers at the end of your matrix number to be the value of block mass. Thus, mass of block is 5 kg. V8 = 395 m/s Bullet Block Figure Q3 (a)
Thank you in advance! A certain mass-spring-damper system has the following equation of motion. x''+ cx' + 100x = f(t) Suppose that the initial conditions are zero and that the applied force f(t) is a step function of magnitude 100. Solve for x(t) for the following three cases: (a) c=10 and (b) c=20, (c) c=50.
5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X; measures horizontal ground motion and co-ordinate X measures the position of the mass m relative to the frame of the seismograph. The mass m = 1 kg, the spring stiffness k = 10 Nm-1 and the coefficient of the damper c = 2 Nsm-¹. Starting from rest, the seismograph is subjected to an oscillatory ground motion given by X; = (10sin2t) mm. For the mass m, (a) set up the equation of motion, (b) calculate the amplitude of the steady state response, and (c) develop an equation describing the amplitude of steady state oscillation as a function of time. To Figure Q5 m
Find the degrees of freedom of the given mechanism.
igure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y 0, and the springs are in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. DE only 225 Your tasks: X k 0 3k a F a M y A Derive an equation of motion for the system in terms of the angular displacement 0, and its derivatives (you should not have y or its derivatives in this equation.) B Derive an equation of motion for the system in terms of the displacement y, and its derivatives (you should not have or its derivatives in this equation. C Assuming there is no external actuator force F acting on the system, write down the total energy H of the system in terms of 0,0 and element constants. Derive an expression for the time derivative H of the total energy. D Transform the equation from part B, which is in y, to another…