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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- The W1= 69.01-lb block shown rests on a smooth plane (coefficient of kinetic friction = 0) with an angle of θ=34∘ from horizontal. It is connected by a flexible inextensible cord that passes around weightless, frictionless pulleys to a support. The W2 =134.93-lb weight is attached as shown. After the system is released from rest, in what distance will the block on the plain attain a speed of 10.0 ft/s?A car of mass 700 kg travels round a horizontal curve of 60 m radius. The centre of gravity of the car is 1.25 m above the ground and the distance between the wheels is 1.7 m. If the limiting coefficient of friction between the tyres and the road is 0.6 determine, with reason, whether the vehicle will skid or overturn when rounding the bend at speed. Hence state the maximum permissible speed to navigate the curve safely.15 kg boxes are being transported around a curve via a conveyor belt as shown to the right. Assuming the curve has a radius of 3 meters and the boxes are traveling at a constant speed of 1 meter per second, what is the minimum required coefficient of friction needed to ensure the boxes don’t slip as they travel around the curve?
- The boxes in the picture (A has a mass of 1.6kg and B has a mass of 4.4kg) are connected with an unstretchable and massless rope. They are released from rest at a level with an angle θ = 50∘. The coefficient of friction between the boxes is μ = 0.24. Friction between box B and the slide can be ignored. a) What is the amount of frictional force between the boxes? b) What is the magnitude of the acceleration of the boxes? c) What is the rope force?Two beads of mass m are initially at rest at the top of a frictionless hoop of mass M and radius R, which stands vertically on the ground. The beads, being strung on the hoop, are constrained to move along the hoop’s circular path. The beads are given tiny kicks, and they slide down the hoop, one to the right and one to the left. What is the largest value of m/M for which the hoop never rises up off the ground? (Given a sufficiently large ratio of m/M the normal force of the beads on the hoop can indeed cause it to jump off of the ground!) Some thoughts/hints about this problem:(a) It is important to think about the direction of the Normal force as the beads move around the hoop. The hoop is exerting a normal force on the beads which are constraining them to stay on the wire as they move around the hoop. The beads are also exerting a normal force on the hoop which is what will make the hoop jump.(b) What happens to the direction of the normal force exerted by the hoop on the beads as…The two blocks shown are originally at rest. Neglect the masses of the pulleys and the effect of friction in the pulleys and between the blocks and the incline. Consider WA = 206 lb and WB = 306 lb.
- In a porter governor the mass of the central load is 18 kgand the mass of each ball is 2kg. the top arms (254) mm while the bottom arms are (304) mm long. The friction of the sleeve is 20 N. If the top arms make 45 deg with the axis of rotation in the equilibrium position, find the range of the speed of the governor in that positionFind the smallest distance d for which the hook will remain at rest when acted on by the force P. Neglect the weight of the hook, and assume that the vertical wall is frictionless.For a technology project, a student has built a vehicle, of total mass 6.00 kg, that moves itself. As shown, it runs on four light wheels. A reel is attached to one of the axles, and a cord originally wound on the reel goes up over a pulley attached to the vehicle to support an elevated load. After the vehicle is released from rest, the load descends very slowly, unwinding the cord to turn the axle and make the vehicle move forward (to the left as shown). Friction is negligible in the pulley and axle bearings. The wheels do not slip on the floor. The reel has been constructed with a conical shape so that the load descends at a constant low speed while the vehicle moves horizontally across the floor with constant acceleration, reaching a final velocity of 3.00î m/s. (a) Does the floor impart impulse to the vehicle? If so, how much? (b) Does the floor do work on the vehicle? If so, how much? (c) Does it make sense to say that the final momentum of the vehicle came from the floor? If…
- In a Porter governor, the mass of the central load is 18 kg and the mass of each ball is 2 kg. The top arms are 250 mm while the bottom arms are each 300 mm long. The friction of the sleeve is 14 N. If the top arms make 45° with the axis of rotation in the equilibrium position, find the range of speed of the governor in that position. 503.2A hammer head H having a weight of 0.26 lb is moving downwards at 40 ft/s when it strikes the head of a nail of negligible mass and drives it into a block of wood as shown. Find the impulse on the nail if it is assumed that the grip at A is loose, the handle has a negligible mass, and the hammer stays in contact with the nail while it comes to rest. [Show work fast , Don't copy]To pass inspection, steel balls designed for use in ball bearings must clear the fixed bar A at the top of their rebound when dropped from rest through the vertical distance H = 36 in. onto the heavy inclined steel plate. If balls which have a coefficient of restitution of less than 0.7 with the rebound plate are to be rejected, determine the position of the bar by specifying h and s. Neglect any friction during impact.