A 1.15 m thin brass rod is bent in half to form a right-angled L, as shown in figure 1. The corner of the L is located at the origin. The rod has a mass per unit length of 440 g/m. Figure 1 a b Figure 2 Find the center of gravity (c.g.) for this geometry. Give the answer in vector notation, &c.g.. ŕ c.g. mî + A different rod with the same mass per unit length, 440 g/m, is bent into an asymmetric Z shape as shown in figure 2. If a = 1.45 m, b = 0.305 m, and c = 0.585 m, what is the c.g. for this geometry? ŕ c.g. mi + mĵ m ĵ

A A wooden plank is placed on top of two identical, solid, parallel cylindrical rollers, as shown in the figure below. The plank has a mass of M= 5.40 kg, and the rollers each have a mass of m= 2.00 kg and a radius of R = 6.00 cm. The plank is pulled by a constant horizontal force F of magnitude 7.20 N applied to the end of the plank and perpendicular to the axes of the cylindrical rollers. The cylinders roll without slipping on a flat surface, and there is also no slipping between the cylinders and the plank. At the instant shown in the figure, the rollers are equidistant from the ends of the plank. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) What is the magnitude (in m/s2) and direction of acceleration of the plank at the instant shown? m/s² magnitude direction --Select--- (b) What is the magnitude (in m/s2) and direction of acceleration of the centers of mass of the rollers at this…

A lamina occupies the part of the disk x² + y < 16 in the first quadrant and the density at each point is given by the function p(x, y) = 4(x2 + y²). %3D A. What is the total mass? D. Where is the center of mass? Submit answer

consider the figure above. consider the small block (M). let say that this inverted cone is rotating vertically or a vertical axis. lets say that the angular speed of this is Vtangential = = r*@ coefficient static friction (block and xone) = Hs. LETS SAY we need to remain this block at its height while spinning (radius of revolution = h*tan theta), FIND: a. Max value of b. min value of

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I Re You're carrying a 3.6-m-long, 24 kg pole to a construction site when you decide to stop for a rest. You place one end of the pole on a fence post and hold the other end of the pole 35 cm from its tip. Part A For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution. How much force must you exert to keep the pole motionless in a horizontal position? Express your answer in newtons. Vo AE F = N Submit Previous Answers Request Answer

6. A yoyo is dropped as shown in the figure below. Neglect air friction. The mass of the yoyo is 0.160 kg, R = 10 cm and Ro = 2.0 cm. a. Show and label the translational forces acting on the yo-yo's center of gravity. Show and label the force(s) exerting non- zero torque(s) about the yo-yo's center of gravity at their point of application. Only show non-zero torques. b. If the linear acceleration of the yo-yo is 2.0 m/s/s, determine the tension of the string.

P1 please help me with the answer and full solution

a. What is the maximum torque applied by the cable? (Give your answer in N m.) b. What is the torque due to the weight of the bridge? (Give your answer in N m.) c. How far can Lancelot ride out along the bridge before the cable breaks? (Give your answer in m.) Note: At his maximum distance, the torque from the cable will equal the torque from both the weight of the bridge and the weight of Lancelot.

You have a summer internship at NASA and are working on plans for a new space station to be launched into orbit around the Earth. The design of the space station is shown. i It is to be constructed in the shape of a hollow ring of mass 52,000 kg. The structures other than the ring shown in the figure have negligible mass compared to the ring. Members of the crew will walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 140 m. The thickness of the ring is very small compared to the radius, so we can model the ring as a hoop. At rest when constructed, the ring is to be set rotating about its axis so that the people standing inside on this deck experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. Your supervisor asks you to determine the following: (a) the time interval during which the rockets must be fired if each…