Two identical masses are attached to frictionless pulleys by very light strings wrapped around the rim of the pulley and are released from rest. Both pulleys have the same mass and same diameter, but one is solid and the other is a hoop. As the masses fall, in which case is the tension in the string greater, or is it the same in both cases? Justify your answer.
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- A pile-driver hammer has a mass of 300 kg and is to be raised 16 m in 4 sec. The total friction on the guides is constant at 400 N. What constant pull must be exerted on the cable?2) Figure 3 illustrates a first block having mass M1 positioned on a horizontal tabletop. The contacting surfaces between the 1st block and the tabletop have a coefficient of kinetic friction Uk. An ideal rope extends horizontally from the 1st block to an ideal pulley and then vertically downward to a 2nd block having mass M2. Initially, the 2nd block is traveling downward with speed Vo. At some later time, the 2nd block has been displaced a distance H and its speed is Vf. Rope Pulley M, Friction M, Figure 3 Determine expressions {M1, M2, Hk, H, g, Vo} for the following: H (a) Work done by gravity onto the system of 2 blocks; (b) Work done by the normal force onto the system of 2 blocks; (c) Work done by tension onto the system of 2 blocks; and (d) final speed, Vt.A vehicle of total weight 40000 + 250*19 Newton is held at rest on a slope of 10 degree during downhill. It has a wheel base of 2.25 m and its center of gravity is 1.0 m in front of the rear axle and 1.5 m above the ground level. Find (a) what are the normal reactions at the wheels? (6) Assuming that sliding does not occur first, what will be the angle of slope so that the vehicle will overturn?
- Instead of using the system shown in Figure.a to raise the mass m2, an engineer proposes to use two simple machines, the pulley and the inclined plane, to reduce the weight required to lift m2. The proposed design is shown in Figure.b. The pulley inertias are negligible. The available horizontal space limits the angle of the inclined plane to no less than 30°. Suppose that the friction between the plane and the mass m2 is negligible. Identify the equation to determine the smallest value m1 that can lift m2. (The answer should be a function of m2 and θ.)Clutch Mechanism 8. In the clutch mechanism shown, two flat circular disks of radius R are mounted so that they can be brought into contact causing a net frictional force. The contact pressure in general depends on the distance from the center and in one specific case may be modeled buy P(r) = Poe-kr, where k is a constant and r is the distance from the center of the discs. The integral cR F = 2m " P(r)rdr gives the total contact force between the discs. Cross-section a. In your own words explain where this formula comes from.The arms of a Hartnell governor are of equal length. When the sleeve is in the mid- position, the masses rotate in a circle with a diameter of 150 mm (the arms are vertical in the mid-position). Neglecting friction, the equilibrium speed for this position is 360 rpm. Maximum variation of speed, taking friction into account, is to be 6% of the mid- position speed for a maximum sleeve movement of 30 mm. The sleeve mass is 5 kg and the friction at the sleeve is 35 N. Assuming that the power of the governor is sufficient to overcome the friction by 1% change of speed on each side of the mid-position, find (neglecting obliquity effect of arms), the (i) mass of each rotating ball (ii) spring stiffness (iii) initial compression of the spring
- Consider the system of two blocks shown in (Figure 1). There is no friction between block A and the tabletop. The mass of block B is 4.80 kg. The pulley rotates about a frictionless axle, and the light rope doesn't slip on the pulley surface. The pulley has radius 0.200 m and moment of inertia 1.30 kg⋅m2. If the pulley is rotating with an angular speed of 8.00 rad/s after the block has descended 1.20 m, what is the mass of block A?Assume that there are no frictional forces between the pulleys and the strings, and the strings are mass-less. The frictional coefficient between the1 kg and 2 kg is 0.05, the frictional coefficient between the 2 kg and 5 kg is 0.1, and the frictional coefficient between the 5 kg and the table is 0.2. (a) Draw free-body diagrams for each mass? (b) Calculate the magnitudes of normal forces and frictional forces?(c) If we release 4 kg and 3 kg from rest what are the accelerations of each mass? (System has two different accelerations)(d) Calculate the tensions in each string?Consider the system of two blocks. There is no friction between block A and the tabletop. The mass of block B is 5.00 kg. The mass of block A is 4.00 kg. The pulley rotates about a frictionless axle, and the light rope doesn’t slip on the pulley surface. The pulley has a mass of 2.00 kg and with a 0.100 m radius. The system is released from rest. (a) What is the angular speed of the pulley when block B falls 1.50 m? (The moment of inertia of the pulley = (1/2)MR^2) (b) How long does it take when block B falls 1.5 m? (block A and block B move with constant acceleration)
- 3. Two blocks, masses m₁ and m2, on a horizontal, frictionless surface are being pulled by a massless, unstretchable rope that goes over a frictionless pulley and is connected to a block of mass m3. Assumer two blocks move together. The coefficient of friction between block 1 and block 2 is . Find the force that block 2 exerts on block 1. 2 [ Free Body Diagrams and Law or Definitio. 3The tension in a pulley belt is 300 N when stationary. The smaller pulley has a diameter of 300 mm and a speed of 1420 rev/min. The coefficient of friction between the belt and the pulley is 0·4 and the angle of lap is 160°. (a) Calculate the tension in each side of the belt at operating speed. (b) Determine the power transmitted when the belt is on the point of slipping. If the pulley system uses a flat belt of CSA 500 mm² and density 1300 kg/m3, determine: (c) The power transmitted, when the mass of the belt is taken into consideration.consider the mass and pulley system in the attached file. mass m1 = 29 kg and mass m2 = 12kg. the angle of the inclined plane is given and the coefficient of kinetic friction between mass m2 and the inclined plane is uk = 0.12. assume the pulleys are massless and frictionless when mass m2 moves a distance 4.94 m up the ramp, how far downward does mass m1 move? d= ?