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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- A mass of ¼-slug is attached to a spring and stretched 1.28 ft from its natural length. From the equilibrium position, the weight is started in motion with an initial velocity of 4 ft/sec in the downward direction. Determine the equation of motion when the force due to air resistance is twice the velocity in pounds.Given a small disk (4-Kg) sliding on top of a smooth table which is connected to an elastic cord having a tension of 8r N (r radial position of the small disk is in meters). If we gave the disk a starting velocity of 5 m/s in the transverse direction when it is at r = 1.5 m, calculate: a- the magnitudes of the radial and transverse components of its velocity when r = 3 m? b- the maximum value of r reached by the disk.bucket of mass m is hanging from the free end of a rope whose other end is wrapped around a drum (radius R, mass M) that can rotate with negligible friction about a stationary horizontal axis. The drum is not a uniform cylinder and has unknown moment of inertia. When you release the bucket from rest, you find that it has a downward acceleration of magnitude a. What are (a) the tension in the cable between the drum and the bucket and (b) the moment of inertia of the drum about its rotation axis?
- There are 3 blocks whose masses are m, 2m and 3m on the smooth surface. The first one has a velocity v and others connected to spring are at rest.The spring force is not impulsive. If the coefficients of restitution and spring are respectively e and k,What is the minimum value of kinetic energy of system?Hint:Equations can be built according to the moving axis with the origin at the center of mass of the bloks connected to the springA ball of mass M is suspended from a vertical rod by two cables. The system rotates around this rod axis at angular velocity w. Assuming that the tensile strength of the upper cable is 2 times the tension of the lower cable. Draw a free body diagram for this ballIn the system shown, a spring is compressed and pushes a mass of 50Kg down the path shown with two different slopes. If the spring has a constant of 25 kN / m, what would have to be the deflection of the spring for the block to reach the limit at 2 m / s? The coefficient of kinetic friction is 0.15 and assume that starting from rest to make the ideal system
- In the system shown, a spring is compressed and pushes a mass of 50Kg down the path shown with two different slopes. If the spring has a constant of 25 kN / m, what would have to be the deflection of the spring for the block to reach the limit at 2 m/s ? The coefficient of kinetic friction is 0.15 and assume that starting from rest to make the ideal systemThe 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation. You are required to obtain an expression for the height of a rider above the ground in terms of both the angle radians the wheel rotates through and the time t, assuming that the rider is initially at a seat that is 2m above the ground surface at the start of the wheel’s journey. Find a general expression for the rate of ascend for this rider in terms of both the angle of rotation and time. Determine how fast this rider is moving vertically when 560 sec and state whether it is ascending or descending. Justify your answer. Find a further general expression for the horizontal displacement of the rider from its initial position with respect to both time and angle of rotation and hence determine…The slender rod shown in Fig 1 has a mass m and length L and is released from rest when θ =0°. Determine the horizontal and vertical components of force which the pin at A exerts on therod at the instant θ = 90°. Use normal and tangent coordinates, assume weight in center of rod, from kinematics, we found ω2 = 3g/L
- 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.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…The pulley in Fig has radius R and a moment of inertia I. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block A and the tabletop is mk . The system is released from rest, and block B descends. Block A has mass mA and block B has mass mB . Use energy methods to calculate the speed of block B as a function of the distance d that it has descended.