A table is composed of a normal area and a sticky area. A disc has thickness d, radius R and made of a material of density p. The disc rolls on the normal area with translational velocity v without loss of energy. Then, the disc enters the sticky area and consequently immediately starts rolling and stops rolling after rolling the total distance l in the sticky area. Find the work done during this process.
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- Pls answer with handwritten solutionsA cord is wrapped around a pulley that is shaped like a disk of mass m and radius r. The cord's free end is connected to a block of mass M. The block starts from rest and then slides down an incline that makes an angle O with the horizontal as shown in the figure below. The coefficient of kinetic friction between the block and the incline is µu. (a) Use the concepts of energy to find an expression for the block's speed as a function of position, d, down the incline. (b) Find the magnitude of the acceleration of the block in terms of µ, m, M, g and O. m,r, MA uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.801 m and 1.25 kg, respectively. A force of constant magnitude F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of F that will accelerate the rod from rest to an angular speed of 6.49 rad/s in 8.61 s. F =
- a small 0.383 kg block slides down a frictionless surface through height h = 0.752 m and then sticks to a uniform vertical rod of mass M = 0.766 kg and length d = 2.34 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ.7 kg 3 kg 53° 49° There is no friction in the system above except between the rope and the pulley so that the rope does not slip on the pulley. The pulley is a uniform spherical shell with a mass of 1.43 kg and radius of 12 cm, and the rope does not slip on the pulley. The system is released from rest. Use work-energy principles to determine how much kinetic energy does the smaller mass have after moving d = 2.3 meters parallel to the ramp? K =The radius of a wheel is 0.890 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. (a) How much rope unwinds while the wheel makes 1.00 revolution? ___m (b) How much work is done by the rope on the wheel during 1.00 revolution? ___J (c) What is the torque on the wheel about its axis due to the rope? ____N⋅m
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