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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?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.
- Expanded.1 deals with the conservation of energy principle. Using the conservation of energy principle to solve this problem is mandatory. Solution using other approaches (equation of motion ...) will be automatically considered false. For the problem related to Expanded.1, sketches of the system showing: • the respective initial and final velocity and position coordinates 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 1-lb collar starts from rest at A and is lifted by applying a constant vertical force F to the cord. The rod is smooth. h=4-ft. 3 ft- Q B A F Determine the Force required for the collar speed to be 2 ft.s¹ at BFundamental.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.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
- 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 (0The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas--pressure, temperature, and density (or quantity per volume): PV = NkBT (or pV = nRT), Figure L₂ Lx 1 of 1 Part A Find the magnitude of the average force (F) in the x direction that the particle exerts on the right-hand wall of the container as it bounces back and forth. Assume that collisions between the wall and particle are elastic and that the position of the container is fixed. Be careful of the sign of your answer. Express the magnitude of the average force in terms of m, vr, and L₂. ► View Available Hint(s) Submit Part B IVE ΑΣΦ ? Imagine that the container from the problem introduction is now filled with N identical gas particles of mass m. The particles each have different x velocities. but their average x velocity squared. denoted1) The first man who studied and partially understood the kinematics of a particle falling in the earth's gravitational field was Leonardo da Vinci (1452-1519). He constructed an apparatus consisting of two vertical boards, hinged together on one side and covered with blotting paper on the inside faces. A leaking water tap lets drops fall down between the boards at presumably equal intervals of time. When a string is suddenly pulled, the boards are clapped together and the positions of the drops on the blotters can be inspected. Suppose that the vertical boards are 3 feet long and the leaking faucet is at such height and the rate of dropping is so regulated that when a drop is just coming out of the faucet, the next or second drop is just at the top of the boards and the sixth drop is at the bottom of the boards, while drops 3, 4 and 5 are between the boards. Calculate the number of drops leaving the faucet per second. ANS. 11.35 drops/secExpanded.4 deals with the conservation of momentum principle. Using the conservation of momentum principle to solve this problem is mandatory. Solution using other approaches will be automatically considered false. For the problem related to Expanded.4, sketches of the system showing: • the respective initial and final velocity and position coordinates 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 B amm F 300 mm 600 mm Knowing the angular velocity of rotation of the bob, 8-kg, is 5 rad/s when the length of the rope is 600mm and the angle is 41°, what is the angular velocity of the rope if the length of the rope becomes 300mm while the angle reduces of 9°?Expanded.4 deals with the conservation of momentum principle. Using the conservation of momentum principle to solve this problem is mandatory. Solution using other approaches will be automatically considered false. For the problem related to Expanded.4, sketches of the system showing: • the respective initial and final velocity and position coordinates 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 B F 300 mm 600 mm Knowing the angular velocity of rotation of the bob, 4-kg, is 3 rad/s when the length of the rope is 600mm and the angle is 44°, what is the angular velocity of the rope if the length of the rope becomes 300mm while the angle reduces of 6°?6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless SupportSEE MORE QUESTIONS