A small mass m slides without friction along the looped apparatus shown in Fig
A marble of mass m and radius r rolls along the looped rough track of the figure.(Figure 1) Ignore frictional losses. Part A What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume r?R. Express your answer in terms of R. Part B What is the minimum value of the vertical height h that the marble must drop if...
1. The small mass m is to slide down the large mass M without friction. The track along which the small block slides is a quarter circle with radius R. The large mass itself is free to move on a frictionless horizontal surface. Initially both masses are at rest with the small mass at the top of the quarter circle, as shown in the figure. (a) (5 Pts.) What is the initial total mechanical energy with respect to the horizontal...
A small block of mass m slides along the frictionless loop the loop track shown below. If it starts from rest at point A, what is the speed of the block at point B? (v = squareroot (10 g R)) What is the net force acting on the block at point C? (Don't forget the gravitational force. (F = -mg (8i + j) At what height above the bottom should the block be released so that the normal force exerted...
a bead slides without friction around a loop-the-loop. a) if the bead is released from a height h=3.5 R, what is its speed at point A is R=30 cm? b) how large is the normal force on it if its mass is 5 g? c) from what minimum height, in terms of R, must the bead be released so that it stays in contact with the loop when it goes around?
A block starts from rest and slides without friction along the surface of a hemisphere of radius R = 1.7 m. As the block slides, eventually it loses contact with the hemisphere. What is the height, h, when the block loses contact with the hemisphere? A block starts from rest and slides without friction along the surface of a hemisphere of radius R = 1.7 m. As the block slides, eventually it loses contact with the hemisphere.What is the height,...
5. A particle of mass m slides without friction and starting from rest down a block of mass M in which the surface is shaped into a quadrant of a circle of radius R. The block also slides without friction on a table top. Choose two suitable generalized coordinates a) Using the Lagrange-multiplier formalism, find the equations of motion of the mass and the block and the reaction force of the block on the mass (ie. the constraint force b)...
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H leading to a circular loop-the loop. The center of mass of the ball will move in a circle of radius R if it goes around the loop. The moment of inertia of a solid ball is Ibull--mr. (a) Find an expression for the minimum height H for which the ball barely goes around the loop, staying...
. A small mass m starts from rest and slides from the top of a fixed sphere of radius r (b) Suppose there is friction between the mass and the sphere with friction coefficient μ,-0.1. what is the minimum angle Emin at which the mass will start to slide along the sphere? (c) The mass is now placed just past this minimum angle and released. The coefficient of kinetic friction k is small but not zero. Does the mass fly...
A bead of mass m slides without friction along a rotating wire in the shape of a parabola with zar2, as shown below. The wire is rotating around the z-axis with constant angular velocity w z=ar2 (a) (0.5 point) Determine the Lagrangian for the system in terms of the coordinate r b) (1 point) Apply the Lagrange Equations to obtain the equation of motion. You (c) (0.5 points) Suppose that the bead is moving in a perfect circle of radius...
A small block with mass 0.0500 kg slides in a vertical circle of radius 0.0760 m on the inside of a circular track. There is no friction between the track and the block. At the bottom of the block's path, the normal force the track exerts on the block has magnitude 3.70 N Part A: What is the magnitude of the normal force that the track exerts on the block when it is at the top of its path? HW...