A uniform chain of length L and mass M lies on a frictionless horizontal table with a very small part hanging from the edge of the table. The chain begins to fall under the weight of the hanging part. Obtain the expression for the velocity of the chain at the instant when the length of the hanging part becomes LIn where n > 1.
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- 0.1/1E: In the figure, two blocks, of mass m1 = 257 g and m2 = 337 g, are connected by a massless cord that-is wrapped around a uniform disk of mass M = 492 g and radius R = 10.1 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T in the cord at the left and (c) the tension T2 in the cord at the right. %3D %3! R. (a) Number i Units m/s^2 (b) Number i Units (c) Number Units eTextbook and Media 898 MAY 1 PDF 8 tv .. DD 80 000 000 888 F9 F10 F11 F6 F7 FB F2 F3 F4 F5 @ 23 2$ & 2 3 4 7 8 9In a rotational equilibrium experiment, a group takes a one-meter ruler with a uniformly distributed mass of 250 grams. A thread will be tied to the ruler 15 cm to the left of the center of mass, swinging the ruler. Then the group places a mass m1 = 170 gr at the 20 cm position on the ruler. Then they place a mass m2 = 155 gr in the 40 cm position. What must be the value of a mass m3 placed at the 15 cm position on the ruler for the system to remain in equilibrium?Please asap
- Consider a disc of mass 0.44kg, with radius 0.5 m on a slope with angle 45 degrees to the horizontal. It has a good grip on the slope and does not slip. The disc is constructed so that its mass per unit area, ρ(r) = r1/2 kg m−2, with r being the radial distance in metres from the axis of the disc. What is the acceleration of the disc down the slope?A hammer is made of a solid sphere and a solid rod of negligible mass attached to the sphere. The radius of the sphere is R=25.0 cm and its mass is m=0.200 kg. The distance from the center of the sphere to the pivot is l=0.800 m. The hammer is released from it is initial position at the angle p=45° with the vertical direction (see Figure below). Find the velocity of its center of mass at the lowest point. The moment of inertia of a solid sphere is 2mR2/5 about the axis through any diameter. mA 4-Kilogram object slides, on a smooth surface, towards the north at a velocity of 5 meters per second. The object hits a fixed pole and is deflected from north to east by an angle of 60° and has a velocity of 5 meters per second. The change in the magnitude of the northward component of the moment of the object is
- In the figure, two blocks, of mass m₁ = 289 g and m₂ = 362 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 533 g and radius R = 11.3 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T₁ in the cord at the left and (c) the tension T₂ in the cord at the right. M (a) Number i (b) Number (c) Number i Units Units Units 081 R NgThe height varies from h to zero according to this function: y(x) = h ( – 1)´ . The constants h and e replace 1.00 m and 3.00 m. There is also a thickness t and a density p. You need two integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the numbers t, h, and p. Ax y(x) X The column at x has a mass Am = (density * volume) = y(x) p t Ax. You add all the Am values to get %3D the total mass M. The sum becomes an integral: М — pt y(x) dx For the center of mass, you add each column's x Am, and divide by M: pt Xc х у(x) dx Calculate xc. The only quantity you'll need is e = 5 m.A block of mass mA=20kg on an inclined plane and a bucket of mass mbucket=16kg are attached to the ends of a massless string passing through a massless pulley as shown in the figure below. The inclined plane makes an angle of θ=46o with the horizontal and the coefficients of kinetic and static friction are μk=0.21 and μs=0.58. The system is initially at rest and a student starts to fill the bucket with balls, each of whose mass is 100 grams, one at a time until the system starts to move. Determine the number of balls the student placed in the bucket. Take g=9.80m/s2 and please note that the number balls must be an integer!