The figure shows a system composed of two bodies, of masses mi and m2, connected through an ideal rope that passes through a pulley, also ideal. Both bodies are on two inclined planes, with the same angle of inclination 0, and coefficients of friction 1 and 2. If mi < m2, find the acceleration of the system. m₂
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- A 25.5 kg mass (m) is suspended by the cable assembly as shown in the figure. The cables have no mass of their own. The cable to the left (T) ) of the mass makes an angle of 0.00 with the horizontal, and the cable to the right (T;) makes an angle (02) of 40.6. If the mass is at rest, what is the tension in each of the cables, T and T; ? The acceleration due to gravity is g = 9.81 m/s?. T T = 123.52 N 123.52 TOOLS x10Q1. m-1 kg m,=4 kg The mechanism set up with m,, m, and weightless pulleys is as shown in the figure. Then, the masses are released. Static and kinetic friction between the inclined plane and m, are 0.6 and 0.5 respectively. What are the accelerations of m, and m,? (g = 10 m / s². Frictions and mass of the pulley are ignored.) Q2. 300 m/s .*........ yatay 100 m/s 320 m x=? A plane is flying horizontally at an altitude of 320 m with 300 m/s speed. It launches its bomb with 100 m/s speed relative to the plane as shown. How many meters away from the castle should the plane launch its bomb to hit the castle. (g=10 m/s², sin370=0.6; cos37°=0.8) Q3. 2 kg The object in the frictionless cone in the figure is making a uniform circular motion. Calculate, a) the normal force that the cone exerts on the object, b) centripetal force applied to the body, c) Find the speed of the object.1. A block of mass m slides down on the surface of a wedge of mass M (see figure below). If there are no frictions between the block and the wedge, and between the wedge and the table, find the acceleration of the wedge, the normal force between the block and the wedge, and the acceleration of m relative to the wedge. Discuss your results in the limit of m<5. There are two masses with unequal weight. The masses are tied by a rope and they are connected over two pulleys as shown in Figure 1. When the system is released, heavier mass accelerates downward and lighter accelerates upward. Assume frictionless pulleys, find the theoretical tension of the thread and the theoretical acceleration. Masses are M1= 6.00 kg and M2= 2.00 kg. Two discs are allowed to move on inclined air table with dimensions a= 11cm, b=17cm, c=60cm. (Hint: You can use free body diagram and M1 b Newton' W.B. M2 s second law of a motion equation (F=m.a) to solve tension, g=980cm/s?.)QI Block A in the figure below weighs 1.40 N, and block B weighs 4.20 N. The coefficient of kinetic friction between all surfaces is 0.30. Find the magnitude of the horizontal force F necessary to drag block B to the left at a constant speed if A and Bare connected by a mass- less cord passing through pulley. FBlock A is sliding down and pulling up both Block B and Block C. Find the accelerations of each body and the tension of rope if the coefficient of friction at Block A is 0.25 and at Block C is 0.35 A= 2000b B= 500 b C: 1000lb 314 AIf the pulleys in the figure are weightless and frictionless, determine the acceleration weight BA ball of mass m, and a block of mass m, are attached by a lightweight cord that passes over a frictionless pulley of negligible mass as in figure (a). The block lies on a frictionless incline of angle 8. Find the magnitude of the acceleration of the two objects and the tension in the cord. (c) The free-body diagram for the block. (The (a) Two objects connected by a incline is frictionless.) lightweight cord strung over a (b) The free-body diagram frictionless pulley. for the ball. m2g sin e mg m2g cose a SOLUTION Conceptualize Imagine the objects in the figure in motion. If m, moves down the incline, m, moves upward. Because the objects are connected by a cord (which we assume does not stretch), the magnitude of the acceleration of m, must be equal to the magnitude of the acceleration of m,. Notice the normal coordinate axes in figure (b) for the ball and the "tilted" axes for the block in figure (c). Categorize We can identify forces on each of the two objects and we are looking for…A Center Raft A person is standing at one end of a uniform raft of length L that is floating motionless on water, as shown above. The center of mass of the person-raft system is a distance d'from the center of the raft. The person then walks to the other end of the raft. If friction between the raft and the water is negligible, how far does the raft nove relative to the water? L/2 B L C d/2 Ⓡ O d Center of Mass of System 2d inweighs 60 N on Earth. (3). A system consists of a pulley (vertical wheel) that is only allowed to rotate (spin). A cord is passed over the pulley and at each end there is a mass attached to the end of the cord. The mass attached on the left is m, =0.6 kg and at the right the mass is m2 = 0.8 kg. a) Calculate both the Tension in the cord and the acceleration of the system. b) What are the accelerations of both masses, if you were to cut the cord? Neglect the friction between cord and wheel,In the adjacent figure, two masses connected by a rope (mass ignorant) pass around the pulley of torque I. Find the acceleration of the two masses while ignoring the friction around the axis of the pulley's rotations. Then discuss the results when mi =Mz |3D missMz M2. M, =0Blocks A, B, and C are placed as in Fig. and connected by ropes of negligible mass. Both A and B weigh 25.0 N each, and the coefficient of kinetic friction between each block and the surface is 0.35. Block C descends with constant velocity. (a) Draw separate free-body diagrams showing the forces acting on A and on B. (b) Find the tension in the rope connecting blocks A and B. (c) What is the weight of block C? (d) If the rope connecting A and B were cut, what would be the acceleration of C?SEE MORE QUESTIONS