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Derive the relation
between the angular momenta HO and HG defined in Eqs. (14.7) and (14.24), respectively. The
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Vector Mechanics for Engineers: Statics and Dynamics
- Two blocks 1 and 2 are connected by a rope over a pulley as shown. The pulley is very light (massless) and rotates with essentially no friction. Calculate the mass of block 1, m1, given that the mass of block 2 is m2=5.5 kg and that block 2 moves and accelerates downwards at 3.57 m/s2 when θ=35∘ and μk=0.4. I think that I need to be using Newtons second law but I just dont know how to solve this. Can you please help?arrow_forward3. Five masses in a region where the acceleration due to gravity is 31.5 ft/s? are as follows, m¡ is 500 gm of mass; m2 weighs 800 g;; m3 weighs 0.222 kgmi mą weighs 3 Ibf & m5 is 0.10 slug of mass. What is the total mass expressed (a) in grams, (b) in pounds, and (c) in slugs?arrow_forwardParvinbhaiarrow_forward
- 3. A thin piece of metal of mass 80 g has the cross section shown in Fig. 17. Find the moment and products of inertia for the axes Ox and Oy. Through what angles must these axes be rotated to coincide with the principal axes? Suppose the body is rotating at a given instant about the Ox axis with an angular velocityarrow_forwardAngular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…arrow_forwardAngular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…arrow_forward
- Channel AB is fixed in space, and its centerline lies in the xy plane. The plane containing edges AC and AD of the channel is parallel to the xz plane. The surfaces of the channel are frictionless and the sphere E has 1.9 kg mass. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. N N E 30° x F 20° B ᎠᏓ C 30°/A 30° Determine the force supported by cord EF, and the reactions RC and RD between the sphere and sides C and D, respectively, of the channel. (Round the final answers to four decimal places.) The force supported by cord EF is The reactions RC and Rp between the sphere and sides Cand D. respectively, of the channel are as follows: RC= RD= z N. 4arrow_forwardfind the center of mass, the velocity of the center of mass, the momentum, and the kinetic energy of the following system: m₁ = 1 kg = 1+21+ 3 k v₁ = 21 + 3ĵ m₂ = 1 kg 7₂ = 1 -j + k v₂ = 2ĵ + 3karrow_forwardA pulley of radius r=67 cm is mounted on a frictionless horizontal axle passing through point O. The moment of inertia of the pulley with respect to point O is l=4.1 kg-m2. A massless cord wrapped around the pulley is attached to a m=6.1 kg block that slides on a horizontal frictionless surface. If a horizontal force of magnitude F=141 N is applied to the block, what is the acceleration of the block? Assume the cord does not slip on the pulley. Round your answer to one decimal place. r, I m Farrow_forward
- For the system given, the bar AB has an angular velocity of wAB=4 rad/s. By use of vector notation, determine the velocity of mass C, and the angular velocity of bar BC when ?=30°.arrow_forwardA 100 kg vehicle initially travels clockwise in a circular path with a radius of 10 m at a speed of 5 m/s. If a counterclockwise couple moment of 100 Nm is applied for 10 s, and the vehicle continues to travel on a circular path at 5 m/s, then the circular path radius must drop to from 10 m to 8 m. True Falsearrow_forwardI need correct answer for this question pleasearrow_forward
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