A mass m moves along the x-axis subject to an attractive force given by 19B2mx/2 and a retarding force given by Bmx, where x is its distance from the origin and B is a constant. A driving force given by mA cos(wt), where A is a lied + e th rticlo alo
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- Fundamental.8 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy...) will be automatically considered false. For the problem related to Fundamental.8 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. A force P is applied at an angle =39 to a 311-kg cart. 0.4 m 0.3 m 0.08 m The acceleration of the cart is 2 m.s-². G B 0.2 m 0.3 m 1. What is the magnitude of the force P (answer on your hand-written work and in the cell below)? 2. What are the reaction at A and B?Fundamental.8 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy...) will be automatically considered false. For the problem related to Fundamental.8 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. A force P is applied at an angle 0 =51 to a 869-kg cart. The kinetic friction coefficient on wheels is 0. P 0 0.4 m 0.3 m 0.08 m The acceleration of the cart is 1.2 m.s2. G B 0.2 m 0.3 m 1. What is the magnitude of the force P (answer on your hand-written work and in the cell below)? 2. What are the reaction at A and B?1 An object of mass 125 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of times the weight of the object is pushing the object up (weight = mg). If we assume that water 40 resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m, find the equation of motion of the object. After how many seconds will the velocity of the object be 90 m/sec? Assume that the acceleration due to gravity is 9.81 m/ sec2. Find the equation of motion of the object. X(t) = %3D
- Fundamental.9 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy...) will be automatically considered false. For the problem related to Fundamental.9 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. The uniform 19 lb beam is initially at rest when the forces FA applied at A (on its left hand-side) is vertical and FB applied at B (on its right hand-side) forms an angle 0=56° with the horizontal. FA FB A В. B 0 12 ft Determine FA (answer in the cell bellow) and FB to make sure that: • the beam has no angular acceleration • its horizontal horizontal acceleration is 1.6-times smaller than its vertical acceleration[Q 4] (a) The equation of a hill path is given by: Y = -0.001 x? + 0.2 x A small vehicle of mass 80 Kg starts from rest at the bottom of hill (point (0,0)) and accelerated toward the top of hill. Find maximum allowable acceleration to keep the vehicle in contact with the surface when reaching top of hill.Fundamental.7 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy ...) will be automatically considered false. For the problem related to Fundamental.7 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. B r C The pendulum bob B has a weight of 5lb and is released from rest in the position shown, 0 =0°. Determine the tension in string BC of length r = 5 ft at the instant the bob reaches point D, =7º.
- Fundamental.7 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy ...) will be automatically considered false. For the problem related to Fundamental.7 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. B The pendulum bob B has a weight of 3lb and is released from rest in the position shown, 0 =0°. Determine the tension in string BC of length r = 4 ft at the instant the bob reaches point D, =4°.Fundamental.7 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy ...) will be automatically considered false. For the problem related to Fundamental.7 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. At the instant 0=50 degrees, the boy's center of mass G has a downward speed VG =11-ft/s. Determine: l-ft G • the rate of increase in his speed, • and the tension in each of the two supporting cords of the swing at this instant (put your answer in the cell below) The boy weights 42-lb. The rope length is 11-ft. Neglect his size and the mass of the seat and cords.Fundamental.7 deals with the equation of motion. The use of the equation of motion to solve this problem is mandatory. Solution using other approaches (conservation of energy...) will be automatically considered false. For the problem related to Fundamental.7 sketches of the system showing: • the respective velocity and acceleration and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. Z Lft 0 The 6-lb man lies against the cushion for which the coefficient of static friction is 0.7. The angle the cushion has is 56° Determine the smallest angular velocity he rotates about the z-axis, at L=9-ft from G, to ensure the man will not slip.
- Draw proper FBDS and derive the differential equations of motion for the system below. Write just the state equations in vector matrix form. mi ft) V Yy, Kz Mz VYz2. 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 (0Zorch, 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.)SEE MORE QUESTIONS