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- A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (i) Identification of the types of ensuing motions of the plank and the rollers, (ii) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown, + +A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (i) Identification of the types of ensuing motions of the plank and the rollers, (ii) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown, 0 + + + wwwxA thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (i) Identification of the types of ensuing motions of the plank and the rollers,
- A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle θ as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (i) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown (ii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (i), and (iii) clear, logical, and systematic manipulations of the relationships you have stated in (ii) above to arrive at the desired results.1. Two identical beads A and B each of mass m connected by a light rod of length rv2 can slide without friction on a fixed ring of radius r. The beads are also connected to fixed points C and D with identical elastic cords each of force constant k and relaxed length rv2 as shown in the figure. Initially the cords coincide with diameters of the ring and the system is in equilibrium. Now the bead-rod assembly is displaced slightly aside and released. Find acceleration of the point of intersection Pof the cords immediately before a cord becomes relaxed. B D Ans = I need to know how this answer mv2 Comes show every step of solution P.The slender, homogeneous rod shown in the figure below is 3 m in length and has a mass of 12 kg. At the instant shown, the rod has an angle to the horizontal of 60-degrees and an angular velocity of 2 rad/s clockwise. Both walls are smooth and provide negligible friction. At the instant shown, what are the reaction forces at A and B? What is the angular acceleration of the rod's center of mass?
- Question A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down slope of angle 9 as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (i) Identification of the types of ensuing motions of the plank and the rollers, (ii) free-body, kinematic and kinetic diagrams with an appropriate global axes system clearly shown, (iii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (ii), and +Consider a steel plate of mass m with dimensions L and w that is equally supported by two ball bearings (one on each end of the shaft shown at pointa A and B). At the instant shown below, the plate is released from rest. Part A: Determine an expression for the plate's angular acceleration magnitude a at this in- stant. (Hint: Use Euler's 2nd Law for pinned rotation and the parallel axis theorem.) Part B: Show that the magnitude of the reaction force at each bearing at this instant is R = mg/8. (Hint: Use the kinematics to relate the acceleration of the center of mass G to the angular acceleration. Use Euler's 1st Law to find the reaction forces with the acceleration you determined. As viewed from the side there are two forces acting on the system weight and two reaction forces both pointing upward at the same location.) A foye مر B L २A garage door is mountedon an overhead rail (Fig.).The wheels at A and B have rustedso that they do not roll, but ratherslide along the track. The coefficientof kinetic friction is 0.52. The distancebetween the wheels is 2.00 m,and each is 0.50 m from the verticalsides of the door. The door is uniformand weighs 950 N. It is pushedto the left at constant speed by a horizontalforce F S , that is applied as shown in the figure. (a) If the distanceh is 1.60 m, what is the vertical component of the force exerted on eachwheel by the track? (b) Find the maximum value h can have withoutcausing one wheel to leave the track.
- A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below. (a) Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way: (iii) statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system in (ii), and (iv) clear, logical, and systematic manipulations of the relationships you have stated in (iii) above to arrive at the desired results. 0 + + ZTTX 1A min cage of mass 4t is to be raised with an acceleration of 1.5m/s2 by a cable passing over a hoist drum of 1.5m diameter. What is the power required when the load has reached a velocity of 6m/s, neglecting the inertia of the drum and weight of the cable, but allowing for bearing friction torque of 3kN at the drum? What is the power required at a uniform velocity of 6m/s5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.