A spherical marble that has a mass of and a radius of rolls without slipping down a loop - the loop track that - has a radius of The marble starts from rest and just barely clears the loop to emerge on the other side of the track. Apply the conservation of mechanical energy to predict the minimum height that the marble must start from to make it around the loop.
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- In a spring controlled governor, the rådiål foPce acting on the balls was 4500 N when the center of the balls were 200 mm from axis and 7500 N when at 300 mm, assuming that the force varies directly as the radius, find the radius of the ball path when the governor runs at 270 r.p.m. Also find what alternation in spring load is required in order to make the governor isochronous and the speed at which it would then run. The mass of each ball is 30 kg.23. In a spring controlled governor, the radial force acting on the balls was 4500 N when the centre of balls was 200 mm from the axis and 7500 N when at 300 mm. Assuming that the force varies directly as the radius, find the radius of the ball path when the governor runs at 270 r.p.m. Also find what alteration in spring load is required in order to make the governor isochronous and the speed at which it would then run. The mass of each ball is 30 kg. 80 mm 60 mm A 80 mm stor lo auiber ors +a b-23. In a spring controlled governor, the radial force acting on the balls was 4500 N when the centre of balls was 200 mm from the axis and 7500 N when at 300 mm. Assuming that the force varies directly as the radius, find the radius of the ball path when the governor runs at 270 r.p.m. Also find what alteration in spring load is required in order to make the governor isochronous and the speed at which it would then run. The mass of each ball is 30 kg. 80 mm 60 mm A 80 mm B stor lo auben oris rade +a b-
- A solid sphere starts from rest at a height of 2.5 meters. rolls down a ramp without slipping, so no friction. The mass of the sphere is 2 kg. It The radius of the sphere is 0.02 m The moment of Inertia of a sphere is: I = (2/5)mr² ) Compute the change in gravitational potential energy when the ball rolls from the top to the bottom of the ramp. Use conservation of energy to compute the angular velocity, oo, in radians/s and the linear velocity in m/s at the end of the ramp. h1A block with a mass of 2.0kg is on a horizontal surface of negligible friction. The block is attached to one end of an ideal spring. The other end of the spring is attached to a vertical wall as shown. The block is pulled back and released from rest. The graph shows the horizontal position x of the block as a function of time t as the block oscillates on the surface. The block is moving to the right when it breaks away from the spring moving with its maximum linear speed. The block reaches an area with a rough surface that has a coefficient of kinetic friction of 0.200. Calculate the distance the block moves on the rough surface as it comes to rest. If he block is then replaced with a cylinder of radius 0.25 m and mass 2.0 kg, which is attached to the spring along an axis through its center. The cylinder is placed on a new surface, which allows it to roll while in oscillation. The cylinder is pulled back until the spring is stretched the same distance as in the previous experiment,…In a governor of the Hartnell type the arms of the bell-crank leversare equal in length, and those carrying the operating masses arevertical when the governor is rotating at its mean speed of 775rev/min, with the masses moving in a circle of 175 mm diameter -The usual central controlling spring is replaced by two paralleltension springs direetly connecting the operating masses. Find(a) the magnitude of each operating mass if a force of 90 N isrequired at the sleeve to maintain it in the mean speed positionwhen the specd is increased from 775 to 800 rev/m in(b) the stiffness, or rate, of each spring if the ratio of sleevemovement to increase of speed is 1 mm to 10 revImin when inthe mean speed position.
- An automobile driver took a curve too fast. The car spun out of control about its center of gravity (CG) and slid off the road in a northeasterly direction. The friction of the skidding tires provided a 0.25 g linear deceleration. The car rotated at 100 rpm. When the car hit the tree head-on at 30 mph, it took 0.1 sec to come to rest. The force exerted by the 100-lb child on her seatbelt harness as a result of the acceleration just prior to impact is 875 lbf 618 lbf 657 lbf 725 lbfThe arms of a Porter governor are each 250 mm long and pivoted on the governor axis. The mass of each ball is 5 kg and the mass of the central sleeve is 30 kg. The radius of rotation of the balls is 150 mm when the sleeve begins to rise and reaches to certain radius at maximum speed. The governor has radius that is 175 mm at mid position. The speed range of the governor is 38 rpm, and the increment in speeds is constant in the three positions. Find : (1) the friction of the load which existed at the sleeve, and (2) the governor radius at maximum speed. The friction is ignore in mid position only.a 4.8 kg block is resting at the top of a 30 degree slope of height 1 m it is attached to a cylindrical pulley of mass 1.7 kg and radius 8 cm by a massless string that unwind as the block slides down hill if the acceleration of the block is 1.9 m per second squared what is its normal force find the velocity at the bottom of the slope using forces and torques
- The radius of the flywheel given in the figure is 600 mm. Its mass is 144The radius of rotation (inertia) of the flywheel, which is kg, is 450 mm. to a mass of 18 kgObject A is suspended from a rope wrapped around the flywheel. system is stagnantbeing released in the (still) state. Object A 1.8 meters downFind the acceleration and velocity of the block when it moves straight.A pair of rods and disc form a triangle with a spring (a spring connects A to C). The spring has a spring constant of 20 N/m and an unstretched length of 1.5m. each rod has a length of 3m and a mass of 10kg. The disk has a mass of 5kg, a radius of .5 and rolls without slipping. The system starts with an angle between the spring and rods of 60 degrees, determine the angular velocity of the rods after it has dropped to a 30 degree angle.Q/A circular disc of mass m and radius r is Qil 'connected to two springs. If it is free to roll onarough horizoutal surface without_slipping, use energy methad to calculat the System natural Trequency.