5. A particle of mass m slides without friction and starting from rest down a block...
As shown below (not to scale), a block of mass starts from rest and slides down a frictionless ramp of height h. Upon reaching the bottom of the ramp, it continues to slide across a flat frictionless surface. It then crosses a "rough patch" on the surface of length d=10m. This rough patch has a coefficient of kinetic friction uK=.1. After crossing the rough patch, the block's final speed is vf=2m/s. What is the height of the ramp? Hint: I...
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,...
A block of mass m starts from rest and slides down from the top of a wedge of height h and length d. The surface of the wedge forms an angle of ? with respect to the horizontal direction. The force of kinetic friction between the block and the wedge is f. How fast is the block traveling when it reaches the bottom of the wedge?
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 block with a mass of 2.5 kg starts from rest at the top of the apparatus shown below. it then slides without friction down the incline, and collides with a spring attached to a wall. The spring has a spring constant of K=120N/m. Using the principle of energy conservation, a. find the initial gravitational potential energy of the block at point A b. find the kinetic energy of the block at point B c. what is the velocity of...
A block of mass 4.4 kg slides 18 m from rest down an inclined plane making an angle of 22 o with the horizontal. If the block takes 10 s to slide down the plane, what is the retarding force due to friction?
A plane pendulum of length L and mass m is suspended from a block of mass M. The block moves without friction and is constrained to move horizontally only (i.e. along the x axis). You may assume all motion is confined to the xy plane. At t = 0, both masses are at rest, the block is at , and the pendulum has angular deflection with respect to the y axis. a) Using and as generalized coordinates, find the Lagrangian...
A bead of mass m slides without friction along a rod, one end of which is pivoted in such a way that the rod can be revolved about the z-axis at a constant angle a, as shown in Fig. 2. The rod is driven with constant angular velocity w about Oz. Use Lagrange method to derive the equation of motion for the bead. Use the distance of m from the origin as generalized coordinate and discuss the motion of the...
A block of mass m = 3.00 kg starts from the rest and slides down a 30.0∘ incline which is 3.60 m high. At the bottom, it strikes a block of mass M = 6.40 kg which is at rest on a horizontal surface (Figure 1). (Assume a smooth transition at the bottom of the incline.) The collision is elastic, and friction can be ignored. (A) Determine the speed of the block with mass m = 3.00 kg after the...