Chose True or False True False The elements of rotational motion are the Mass, Spring, Friction. the notation represents the feedback path in closed loop system is c(t). If a system is subjected to step input, the type of static error coefficient performs the function of controlling steady state error is position.
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- Problem 2 Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let la be the length of the spring at equili brium, and r be the elongation. The block oscillates and at the same time is rotating around origin 0, in the plane of the inclined, by a variable angular velocity . 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa- tions) k reference plane m o'A wheel of radius a, mass m, and moment of inertia I is pulled along a horizontal surface by application of a horizontal force F to a rope unwinding from an axle of radius b as shown in the figure. There is a friction force between the wheel and the surface such that the wheel rolls without slipping. a. What is the linear acceleration of the wheel? b. Calculate the frictional force that acts on the wheel (Use Newtonian formalism). b aPlease help with this homework problem. Show all work
- Learning Goal: To understand the Equipartition Theorem and its implications for the mechanical motion of small objects. In statistical mechanics, thermal energy is the random motion of the microscopic world. The average kinetic or potential energy of each degree of freedom of the microscopic world therefore depends on the temperature. If heat is added, molecules increase their translational and rotational speeds, and the atoms constituting the molecules vibrate with larger amplitude about their equilibrium positions. It is a fact of nature that the energy of each degree of freedom is determined solely by the temperature. The Equipartition Theorem states this quantitatively: The average energy associated with each degree of freedom in a system at absolute temperature T is (1/2)k³T, where KB = : 1.38 × 10-2³ J/K is Boltzmann's constant. A "degree of freedom" corresponds to any dynamical variable that appears quadratically in the energy. For instance, (1/2)mv² is the kinetic energy of a…ASAP PLEASE, show all work and do all steps (a through c) A horizontal pole of weight wp= 230 N and length L=5.00 m is hinged to a vertical wall on its left end. The pole is supported by a wire that connects the right end to a point on the wall directly above the left end of the pole as shown in the figure. A physics student of weight ws = 620N hangs from the right end (not shown). The wire will break if the tension exceeds 1140 N. a) Draw a Free-Body diagram for the pole. b) What is the minimum height above the hinge (h) that the wire must be attached to the wall to avoid breaking the wire? (m) c) What is the magnitude of the horizontal force that the hinge exerts on the pole? (N)question d and e please For any vector quantity, be sure to always include the magnitude and direction(teacher asked)
- Jerry's great grandmother's vitrola plays records at 78 roatations per minute (rpm). Describe what will happen if Jerry starts the vitrola on a friction free table. Justify your answer.A person has a mass of 45 kg is running with a velocity of 12.0 m/s. All of a sudden, the person plants their feet and stops abruptly in 3.75 m. This was some mighty agressive stoppage power! Your answer to part (a) may reflect that. a. What was the coefficient of friction between their shoes and the ground in order to do so? b. If it took place in 0.625 seconds how much power was expended by friction on the person?The apparatus below is a massless wheel of radius that is mounted to a frictionless axle. A small, dense piece of clay with mass is glued to edge of the wheel as shown. Another mass hangs from a massless string that is wrapped around the wheel. We can assume the string is inextensible and does not slip, and the system is in a uniform gravitational field. In terms of the rotation angle of the wheel, write down the total potential energy of the system of both masses. Take note of any constraints that you use to write this as a 1D problem.
- Suppose you start an antique car by exerting a force of 350 N on its crank for 0.16 s.Randomized Variablesf = 350 Nt = 0.16 sd = 0.22 m What angular momentum is given to the engine if the handle of the crank is 0.22 m from the pivot and the force is exerted to create maximum torque the entire time?30⁰ Given: Using the provided information, compete the following problems. NOTE: Find: The system shown is initially in static equilibrium and motionless. Submitted responses shall be to 4 significant figures. Do NOT use scientific notation. 1. The maximum magnitude of the Weight-W that will not initiate motion is 2. The minimum magnitude of the Weight-W that will not initiate motion is 3. Assume the 50LB-Block is on the verge of moving up the inclined plane. The magnitude of internal force in the rope (near the 50LB-Block) is 4. Assume the 50LB-Block is on the verge of moving down the inclined plane. The magnitude of internal force in the rope (near the 50LB-Block) is 50 lb Hs=0.30 W H, = 0.20 LB. LB. LB. LB.