rolling wheel, pulley and block: x(t) O(t) m, a m, is a uniform disk with mass m,, radius r rolls without slip on slope with angle alpha Block m2hanging from massless moving pulley Find equation of motion of the system in terms of x(t) m, y(t)
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- Consider a disc of mass, M 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 equation describing the linear acceleration of the centre of mass of the disc down the slope in terms of the angular acceleration of the disc.A ladder of length 2L and mass M is positioned on level ground leaning against a wall such that the angle between the ladder and the horizontal is @. The coefficient of static friction between the ladder and the wall and between the ladder and the ground is jistatic = 0.66. The centre of mass of the ladder is halfway along it. For the ladder to be in mechanical equilibrium: Consider torques about the centre of the ladder. In which direction (into or out of the page) does the torque due to each of the 5 forces force act?Write down an equation for the sum of the torques about the centre or mass of the ladder and then use your equation for the torques to derive an expression for tan o in terms of the magnitudes of the forces actingDynamics of rigid bodies Problem 5
- A professor's office door is 0.99 m wide, 2.2 m high, 4.2 cm thick; has a mass of 27 kg, and pivots on frictionless hinges. A "door closer" is attached to door and the top of the door frame. When the door is open and at rest, the door closer exerts a torque of 5.6 N*m. What is the moment of inertia of the door? If you let go of the open door, what is its angular acceleration immediately afterward?The beam, uniform in mass, M = 47.6 kg and length L = 10.2 m, hangs by a cable supported at point B, and rotates without friction around point A. On the end far of the beam, an object of mass m = 24.3 kg is hanging. The beam is making an angle of θ = 30.9° at point A with respect to the + x-axis. The cable makes an angle φ = 21.1° with respect to the - x-axis at B. Assume ψ = θ + φ. a. Enter an expression for the lever arm for the weight of the beam, lB, about the point A. b. Find an expression for the lever arm for the weight of the mass, lm. c. Write an expression for the magnitude of the torque about point A created by the tension T. Give your answer in terms of the tension T and the other given parameters and trigonometric functions. d. What is the magnitude, in newtons, of the tension in the cable? e. Enter an expression the horizontal component of the force, Sx, that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables…A spade is modelled as a uniform rod, of mass 2kg and length 90cm, attached to a uniform square lamina, of side 20cm and mass 0.5kg. A gardener holds the spade horizontally with hands 30cm and 60cm from the end of the rod. Find the vertical forces exerted by the gardener's hands. Im stuck on this question. Pls help me
- A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I= cMR2. As shown in the figure, the sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side, but now with no friction at all between the sphere and the ramp. What height does the sphere reach?2: A heavy cask (full of wine!) sits on an inclined plane. It is held in place by a rope that is attached to the cask and to a hook further up the inclined plane (at A). The rope comes off of the cask, tangent to the cask. What is the maximum value of angle theta before the cask begins to slip? Also, what is the tension in the rope when slipping is impending? The mass of the cask is 60 kg, and the coefficient of static friction between the inclined plane and the cask is 0.3. Finally,if the inclined plane became icy, and the rope didn’t break as the cask slipped, what would be common about the lines of action of the W, N and T force vectors once equilibrium was reestablished? Hint: draw a FBD.A machine part has the shape of a solid uniform sphere of mass 220 gg and diameter 3.50 cmcm . It is spinning about a frictionless axle through its center, but at a point at the top of the sphere, it is scraping against metal, resulting in a friction force of 0.0200 NN at that point. Find the angular acceleration of the sphere, including the direction (a positive value would indicate the +z direction and a negative value would indicate the -z direction).
- The photo shown was theset-up of the chocolateexperiment you haveconducted before. What mechanical property wastested? Can you relate thisconcept to the suspensionbridges? How?The shaft in the figure, carrying three unbalanced masses, is rotating at a constant speed hızla = 10 r / s. Find the balancing values (kg.mm) and their positions in case of balancing in DI and DII planes.Please reply as soon as posible, thanks! I don´t have much time:( Static Problem: The spool shown in the figure has a weight of WAB = 27,50 N, and its center of gravity is located at its geometric center O, the spool has a larger radius R=0,17 and an inner radius r=0,13, and it has a coiled rope. Block C has a uniform weight WC= 60 N. Consider the friction between block C and the top of the spool at A, between the spool and the surface at point B and between the rope and pulley D, the friction coefficients are respectively: μs@A=0,30, μs@B =0,45 and μs@D=0,35. The chord is parallel to the plane. Carry out: a) The free-body diagrams of the block and the reel. b) The calculation of the maximum value of P that can be applied without losing the equilibrium of the system.