A man of mass m, 75.0 kg holds on to a rope that passes through three pulleys and is attached to the ceiling at point A as shown in the figure. One of the pulleys is connected to a box of mass m, = 280 kg that slides on a frictionless plane inclined at an angle 0 = 45.0"with respect to the horizontal. The pulleys are massless and frictionless and the system is subject to the regular force of gravity.
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- A system comprised blocks, a light frictionless pulley, and connecting ropes is shown in the figure. The B block has a mass of 9.3 kg and is on a perfectly smooth horizontal table. The surfaces of the A block, which has a mass of 8.2 kg, are rough, with μk=μk= 0.25 between the block and the table. If the C block with mass 9.9 kg accelerates downward when it is released, find its acceleration.A Block A with mass mĄ rests on a horizontal tabletop, while block B with mass mg hangs from a string of negligible mass that passes over a pulley and attaches to block A, as shown above. The pulley has negligible mass and rotates with negligible friction about its axle. The blocks are at rest due to friction between block A and the tabletop. The coefficient of static friction between block A and the tabletop is u (mu), where u < 1.The frame is made from uniform rod which has a mass p per unit length. A smooth recessed slot constrains the small rollers at A and B to travel horizontally. Force P is applied to the frame through a cable attached to an adjustable collar C. Determine the magnitudes and directions of the normal forces which act on the rollers if (a) h = 0.24L, (b) h = 0.50L, and (c) h = 0.91L. The forces will be positive if up, negative if down. Evaluate your results for p = 1.8 kg /m, L = 575 mm, and P = 48 N. What is the acceleration of the frame in each case? (a) Answers: (b) L (c) A h = 0.24L: h = 0.50L: h = 0.91L: L A = A A = B i i i P B N₁ B N, B N, i i N₁ª N,9 N₁9 i i m/s m/s m/s
- A speedboat with a mass of 545 kg545 kg (including the driver) is tethered to a fixed buoy by a strong 32.7 m32.7 m cable. The boat's owner loves high speed, but does not really want to go anywhere. So the owner revs up the boat's engine, makes a lot of noise, and runs the boat in circles around the buoy with the cable supplying all the necessary centripetal force. When the tension of the cable is steady at 13700 N,13700 N, with what force is the boat's engine pushing the boat? Different physics textbooks treat drag force somewhat differently and use different formulas. For the present purpose, take the water's drag force on the boat to be (450 kg/m)×?2,(450 kg/m)×v2, where ?v denotes the boat's speed. Ignore any drag force on the cable.A speedboat with a mass of 505 kg (including the driver) is tethered to a fixed buoy by a strong 29.7 m cable. The boat's owner loves high speed, but does not really want to go anywhere. So the owner revs up the boat's engine, makes a lot of noise, and runs the boat in circles around the buoy with the cable supplying all the necessary centripetal force. When the tension of the cable is steady at 12300 N, with what force is the boat's engine pushing the boat? Different physics textbooks treat drag force somewhat differently and use different formulas. For the present purpose, take the water's drag force on the boat to be (450 kg/m) × v², where v denotes the boat's speed. Ignore any drag force on the cable. force: N & TOOLS x10A 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!
- (a) A block of mass m = 3.10 kg is suspended as shown in the diagram below. Assume the pulley to be frictionless and the mass of the strings to be negligible. If the system is in equilibrium, what will be the reading of the spring scale in newtons? Spring Scale m (b) Two blocks each of mass m = 3.10 kg are connected as shown in the diagram below. Assume the pulley to be frictionless and the mass of the strings to be negligible. If the system is in equilibrium, what will be the reading of the spring scale in newtons? Spring Scale (c) A block of mass m = 3.10 kg is in equilibrium on an incline plane of angle e = 34.0° when connected as shown in the diagram below. Assume the mass of the strings to be negligible. If the system is in equilibrium, what will be the reading of the spring scale in newtons? Spring Scale mThe sketch shows a coin at the edge of a turntable. The weight of the coin is shown by the vector W. Two other forces act on the coin—the normal force and a force of friction that prevents it from sliding off the edge. Draw in force vectors for both of these.A uniform plank of length 2.00 m and mass 31.5 kg is supported by three ropes, as indicated by the blue vectors in the figure below. Find the tension in each rope when a 715–N person is d = 0.500 m from the left end. magnitude of T1 N magnitude of T2 N magnitude of T3 N