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Vector Mechanics for Engineers: Statics and Dynamics
- 4. Rod OA rotates about O in a horizontal plane. The motion of the 0.5-lb collar B is defined by the relations r = 10 + 6 coSn t and e = 1 (4t? – 8t), where r is expressed in inches, t in seconds, and 0 in radians. Determine the radial and transverse components of the force exerted on the collar when (a) t= 0, (b) t = 0.5 s. Barrow_forwardPROBLEM 3.12 An object is launched at a speed of 20.0 m/s from the top of a tall tower. The height y of the object with respect to the base of the tower as a function of the timet elapsed from launch is y(t) = -4.90t² + 19.32t + 60, where y is in meters and t is in seconds. Determine: 13. the height H of the tower. 50 m c. 70 m d. 80 m а. b. 60 m 14. the launch angle. с. 75.35° d. 77.35° а. 71.35° b. 73.35° 15. the horizontal distance traveled by the object before it hits the ground. с. 32.28 m d. 34.28 m a. 28.28 m b. 30.28 marrow_forward2. Show that the gravitational self-energy (energy of assembly piecewise from infinity) 3GM? of a uniform sphere of mass M and radius R is U = - 5Rarrow_forward
- 3. A particle of mass m is at rest at the end of the spring (force constant k) hanging from a fixed support. At t=0, a constant downward force F is applied to the mass and acts for a time to. Show that after the force is removed, the displacement of the mass from its equilibrium position (x=xo, where x is down) is F -[cos @, (t-t,)- cos w,t] k x- X, where w = k / m.arrow_forwardQ2.A warplane turns left at an orbit with a radius of R = 500 m at a speed of 1600 km /h parallel to the ground. The angular velocity vector of the turbine rotor is in the negative direction (in front of the plane) with the speed 90000 rpm. The distance between the bearings of the rotor is 1.2 m and the total moment of inertia of the rotor is 220 kg.m? ( the rotor is acceppted as a disc and it is located in the middle of the bearings). The total forces (weight of the rotor + gyroscopic impact forces) acting on the front and rear bearings of the rotor during this rotational motion of the aircraft shall be determined. The total mass of the rotor is m = 1800 kg.arrow_forward5. A 2-kg sphere is attached to a massless rigid rod attached to a fixed pivot point O. The rigid rod and mass rotate in the horizontal plane. A moment is applied to the rod of magnitude M = 0.5t² N. m, where t is in seconds. The length of the rod is 0.5 m. Determine the speed of the sphere after the moment is applied for 5 seconds. M(t)arrow_forward
- ! Required information 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 1.6 kg mass. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. N J N D 30° + E 30° X F A 30° 20° B Determine the force supported by cord EF, and the reactions RC and Rp 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 N. The reactions Rcand Rp between the sphere and sides C and D, respectively, of the channel are as follows: RC= RD= Zarrow_forwardPin B weighs 0.1kg and is free to slide in a horizontal plane along therotating arm OC and along the circular slot DE of radius b=500mm.Neglecting friction and assuming that θ= 15 rad/s andθ=250 rad/s2 for the position θ= 20o , determine for that position(a) the radial and transverse components of the resultant forceexerted on pin B, (b) the forces P and Q exerted on pin B,respectively, by rod OC and the wall of slot DE.arrow_forwardTwo identical giant flywheels are on 2 identical slopes at an angle alpha = 20 deg. One flywheel is rolling on its inside shaft of diameter d1 = 3 ft, and the second flywheel is rolling without slipping on its outside diameter d2 = 5 ft. They are both released from rest. The weight of the flywheel is W = 8 lbs Knowing that flywheel 1 attains a speed of v = 7.0 ft/s in t = [t] s, (if t doesn't show take any t between 5 and 10 sec) find the radius of gyration of the flywheels, following those steps: b. Find omega final c. Find the angular impulse at the point of contact between the shaft and the slope. d. Write the formula to find the final momentum. e. Solve for k, using the principle of angular impulse and momentumarrow_forward
- 4. According to the principle of conservation of energy, under the action of ... . force, the sum of potential and kinetic energy of a particle remains constant. (1 M) a. dissipative force b. conservative force c. frictional force d. non-conservative force 5. Work-energy principle to be useful in determining the change in the speed of a particle during a given displacement. а. True (1 M) b. False 6. If the collision is elastic, the kinetic energy before collision is always equal to the kinetic energy after collision. (1 M) а. True b. Falsearrow_forwardQ4. In the image shown below, according to the provided datum line, determine the gravitational potential energy of the 6.0-kg block. The radius r = 2.1 m. Negative sign must be included if the energy is negative. Please pay attention: the numbers may change since they are randomized. Take g = 9.81 m/s². Your Answer: Answer 1 Datumarrow_forwardA force P is applied at an angle 0 =10 to a 942-kg cart. P G 0.4 m 0.3 m В 0.3 m * 0.2 m → 0.08 m The acceleration of the cart is 5 m.s 2. 1. What is the magnitude of the force P (answer on you hand-written work and in the cell bellow) ? 2. What are the reaction at A and B?arrow_forward
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