Chapter 18, Problem 3RQ

(a) What kind of equation is it?(b) Is it linear or non-linear?(c) Is it a coupled system or uncoupled?

What kind of system is presented in Figure 2? Open loop or closed loop?

What are the control hardware shown in the Figure?

Question 1. A tube rotates in the horizontal ry plane with a constant angular velocity w about the z-axis. A particle of mass m is released from a radial distance R when the tube is in the position shown. This problem is based on problem 3.2 in the text. R m 2R Figure 1 x a) Draw a free body diagram of the particle if the tube is frictionless. b) Draw a free body diagram of the particle if the coefficient of friction between the sides of the tube and the particle is = k = p. c) For the case where the tube is frictionless, what is the radial speed at which the particle leaves the tube? d) For the case where there is friction, derive a differential equation that would allow you to solve for the radius of the particle as a function of time. I'm only looking for the differential equation. DO NOT solve it. 1 e) If there is no friction, what is the angle of the tube when the particle exits? • Hint: You may need to solve a differential equation for the last part. The "potentially useful…

Question 2. A smooth uniform sphere of mass m and radius r is squeezed between two massless levers, each of length 1, which are inclined at an angle with the vertical. A mechanism at pivot point O ensures that the angles & remain the same at all times so that the sphere moves straight upward. This problem is based on Problem 3-1 in the text. P P r Figure 2 a) Draw appropriate freebody diagrams of the system assuming that there is no friction. b) Draw appropriate freebody diagrams of the system assuming that there is a coefficient of friction between the sphere and the right lever of μ. c) If a force P is applied between the ends of the levers (shown in the diagram), and there is no friction, what is the acceleration of the sphere when = 30°

If you had a matrix A = [1 2 3; 4 5 6; 7 8 9] and a matrix B = [1 2 3], how would you cross multiply them i.e. what is the cross product of AxB. what would be the cross product of a dyadic with a vector?

Problem 3: The inertia matrix can be written in dyadic form which is particularly useful when inertia information is required in various vector bases. On the next page is a right rectangular pyramid of total mass m. Note the location of point Q. (a) Determine the inertia dyadic for the pyramid P, relative to point Q, i.e., 7%, for unit vectors ₁₁, 2, 3.

Can you solve for v? Also, what is A x u

The external loads on the element shown below at the free end are F = 1.75 kN, P = 9.0 kN, and T = 72 Nm. The tube's outer diameter is 50 mm and the inner diameter is 45 mm. Given: A(the cross-sectional area) is 3.73 cm², Moment inertial I is 10.55 cm4, and J polar moment inertial is 21.1 cm4. Determine the following. (1) The critical element(s) of the bar. (2) Show the state of stress on a stress element for each critical element. -120 mm- F