A wedge of mass 2m placed on a rough surface, its part AB is circular of radius R. A small block of mass m is released from rest at A. Find minimum value of friction between wedge and ground so that wedge remains at rest. m smooth R 2m B rough (A) 3mg mg (B) 5mg (C) 3mg (D) 2
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- A skateboard of mass m rests on the top of a hemispheric dome of radius R. After giving the skateboard a small kick, imparting an initial speed of vo, it begins rolling down the dome. Let the angle 0 indicate the location of the skateboard as it rolls down the surface of the dome. R 1. Eventually, the skateboard will lose contact with the dome. Given m, R, vo, and g, find the angle 0. at which the skateboard loses contact. Express your answer symbolically (i.e. without numbers). Check your work. Suppose you choose m = 1.5 kg, vo = g = 9.81 m/s. In this case, your answer should evaluate to 0. = 34.2°. 4.5 m/s, R = 4.3 m, and 2. Given m, R, and g, determine the range of speeds for which it is impossible to remain in contact with the wall at all.Two solid spheres of radius R and mass m are initially separated by a distance d such that the two centres of mass are separated by d+3R as shown below. The spheres are initially at rest, but the gravitational force accelerates them towards each other until they collide.a) Calculate the initial mechanical energy of the system.b) Calculate the gravitational potential energy of the system at the moment they collide.c) Derive an expression for v. State carefully what physical law you are applying.d) Show that, in the limit d >> R, the velocity v is independent of d.Among the elderly population, a sideway fall is a most frequent cause of hip fracture. An old man of mass 65 kg and height 1.7m was sent to Prince of Wales Hospital due to sideway fall. He slipped and fell laterally down with a straight body. Before falling, his centre of mass was 0.9 m above ground. His centre of mass was on the ground at the end of the fall. The radius of gyration about the anterior-posterior axis at his centre of mass was 0.55 m. (a) Calculate the initial potential energy before his fall. (b) Assuming his potential energy would be converted to linear kinetic energy of his centre of mass and rotational kinetic energy about his centre of mass, calculate the impact velocity v of his centre of mas right before he hit the ground. C. M. 1.7m 0.9m
- The 11 kg disk has an angular velocity of w = 20 rad/s. (Figure 1) Figure 400 mm 500 mm 200 mm- A B ⒸO 500 mm с P (N) 5 2 1 of 1 -t(s) Part A If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The coefficient of kinetic friction at B is μ = 0.4. Neglect the thickness of the brake. Express your answer to three significant figures and include the appropriate units. t = 0 Submit Value μA Provide Feedback Request Answer Units ? Next >The cylindrical plug A of mass mA = 2.7 kg is released from rest at B and slides down the smooth circular guide. The plug strikes the block C of mass mc = 2.1 kg and becomes embedded in it. Calculate the distances which the block and plug slide before coming to rest. The coefficient of kinetic friction between the block and the horizontal surface is uk = 0.38 and the distance r = 2.08 m. Hk Answer: s= i mc A MA B mNumber 4 needs answered
- An object with mass M slides across a frictionless half-circular slide of radius R. The object is initially held stationary at the top of the slide. The initial height is, hi = R. The mass is released and slides down, around the bottom, and back up the other side. The radius of the slide is R = 5.79 m and the mass of the object is M = 37 kg. When the object is moving up the slide, at an angle θ = 18o from the vertical, what is the normal force on the object?A puck of mass m = 1.10 kg slides in a circle of radius r = 19.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 4.10 kg by a cord through a hole in the table. What speed keeps the cylinder at rest?50 300g 10 10 25 cm 3) A kinetic sculpture consists of two rods of negligible mass, each suspended 10 cm from their ends. The longer rod has a length of 50 cm and the shorter has a length of 25 cm. If the square mass is 300 g, then what must the triangular mass and circular masses be to achieve equilibrium?