What a force which is dependent of the path and does not depend only upon initial and final positions called?

D 3.4-5. Consider the following problem, where the value of c, has not yet been ascertained. Maximize Z = c,x1 + 2xz, subject to 4x1 + x, < 12 X - x, 2 2 and X 20, X2 2 0. Use graphical analysis to determine the optimal solution(s) for (x1, X2) for the various possible values of c1.

Drop-load (III) context We want to lower a suspended load in a controlled way, so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on an inclined surface. Information The masses of charges A and B are known.The pulley is a solid cylinder (or disc) of mass mp and radius R which can turn without friction.The surface on which mass A is placed is horizontal.There is friction between mass A and the surface on which it is placed, the coefficient of friction is uc.Mass A is on a surface tilted by an angle delta.The rope attached to mass A is perfectly parallel to the surface on which the mass is placed. Modelization Create a model for the acceleration of mass B given the known parameters of the problem that are relevant. Mass of load A: 70kg; Mass of the suspended load (B): 82kg; Pulley mass (mp): 52kg Pulley radius: 0.46m Coefficient of friction: 0.12…

Q4.

What a force which is independent of the path and depends only upon initial and final positions called?

A uniform beam of length, L, and mass, M, is freely pivoted at one end about an attachment point in a wall. The other end is supported by a horizontal cable also attached to the wall, so that the beam makes an angle phi with the horizontal as shown below. To answer the questions below, find algebraic expressions for the tension in the cable, the angular acceleration of the beam, should the cable break, and the resulting angular velocity as the beam falls through the vertical position. A. If L = 2.4 m, M = 5 kg, and phi = 45o, then what is the tension in the cable? B. If the cable snaps, what is the angular acceleration about the pivot point? C. What is the angular velocity of the falling beam, just as it hits the wall?

Using the equation of motion and please include free body diagram. thank you!

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)

full solution pls no short cut show the process

I need a clear and fast answer within 20 minutes. Thank you