A bob of mass 30 g suspended by a string is able to complete a vertical circular loop at a place where g=10 m/s2. If the maximum change in its PE during the motion 0.6 J, the radius of path is-
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A bob of mass 30 g suspended by a string is able to complete a vertical circular loop at a place where g=10 m/s2. If the maximum change in its PE during the motion 0.6 J, the radius of path is-
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- The system is released from rest with the spring initially stretched 2.8 in. Calculate the velocity v of the cylinder after it has dropped 1.5 in. The spring has a stiffness of 4.1 lb/in. Neglect the mass of the small pulley. k = 4.1 lb/in 80 lb=J (e) (b) Fe= () 6. A pendulum that consists of a ball (m = 1.50 kg) attached to a light cord rotates in a circular path of radius r = 0.800 m at constant speed v, as shown in Figure. Here the angle 0 = 65°, and we ignore air friction and assume the mass of the light cord is negligible. (a) Calculate the tension T in the cord. = L. (b) Calculate the centripetal force acting on the ball. = 'd (c) Calculate the velocity v of this uniform circular motion. Answers:The car is fully loaded with passengers and has a total mass of 575 kg. At point A, the car is at the lowest point in a circular arc of radius r1 = 12.4 m. At point B, the car is at the highest point of a circular arc of radius r2 = 17.3 m. (a) If the car has a speed of 25.0 m/s at point A, what is the magnitude of the force (in N) of the track on the car at this point? (b) What is the maximum speed (in m/s) the car can have at point B in order for the car to maintain contact with the track at all times (that is, so that it does not "jump" off the track)?
- 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 200 kg mass hangs from a 300 m cable on Mars (g=3.71 m/s2). It is displaced left from equilibrium along an arc with length 30 m and released at t = 0. What is its position relative to equilibrium when t = 20 s? What is its acceleration?A 1.5-lb slider is propelled upward at A along the fixed curved bar which lies in a vertical plane. If the slider is observed to have a speed of 10.6 ft/sec as it passes position B, determine (a) the magnitude N of the force exerted by the fixed rod on the slider and (b) the rate v at which the speed of the slider is changing (positive if speeding up, negative if slowing down). Assume that friction is negligible. 29 2.8' Answers: N = Ib i ft/sec?
- A carousal has a radius R=7 m, with cables tying the seats being L=10 m long. What should be the speed of the seats so that the cables make an angle of A= 19 degrees with the vertical.A 35.0 kg child is on a swing following a circular path with a radius of 3.25 m. As the swing passes through the lowest point of the circular path, the seat exerts a force of 480 N [up] on the child, what is the speed of the swing at that point?A long limp spring is hung from a beam; the spring's bottom is 660 mm above the table. A 0.50 kg cylinder is hooked to the spring's bottom while the spring hangs relaxed. When the cylinder is dropped, it turns around just above the table, where the spring's bottom had been stretched to 10 mm above the table. What is the cylinder's velocity, half-way to the bottom turn-around?