A drum is used to drag a [m^]-kg block A up the slope (0 = [0]°). The coefficients of static and kinetic friction between the block and slope are 0.5 and 0.3 respectively. The [mp]-kg drum has a radius of 0.6 m and a radius of gyration of [k] mm. A constant torque of [t] Nm (CCW) is supplied to the drum. Assume the drum pivot is frictionless. (a) Draw clear free body diagrams of block A and the drum.
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- If a rigid body is subject to planar motion in the xy-plane, then the angular momentum about the rigid body's center of mass can be expressed as the body's angular velocity times the body's moment of inertia about the z-axis through the center of mass plus the body's angular velocity time the sum of two products of inertia. If a rigid body is subject to planar motion in the xy-plane, then the angular momentum about the rigid body's center of mass can be expressed as the body's angular velocity times the body's moment of inertia about the z-axis through the center of mass plus the body's angular velocity time the sum of two products of inertia. True FalseA glass bead of diameter 1.70 mm and density 2.89 g/cm3 spins uniformly at a rate of 3n rad/s along a vertical nylon thread that cuts through an axis running through its center. Assuming the bead to be a regular solid sphere (Icom = (2/5)MR²) and neglecting the hole in the middle where the thread goes, report the kinetic energy of the bead in joules. 3.05 x 10-9 J 9.54 x 10-15 J O 7.63 x 10-10J 9.54 x 10-11 JDuring a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 120 N to the tire's rim. The mass of the wheel is 1.70 kg and, for the purpose of this problem, assume that all of this mass is concentrated on the outside radius of the wheel. The diameter of the wheel is 50.0 cm. A chain passes over a sprocket that has a diameter of 9.00 cm. In order for the wheel to have an angular acceleration of 3.60 rad/s2, what force, in Newtons, must be applied to the chain? (Enter the magnitude only.) N
- 10.58 A 50.0 kg grindstone is a solid disk 0.520 m in diam- eter. You press an ax down on the rim with a normal force of 160 N (Fig. P10.58). The coefficient of kinetic friction between the blade and the stone is 0.60, and there is a constant friction torque of 6.50 N m between the axle of the stone and its bearings. (a) How much force must be applied tangentially at the end of a crank handle 0.500 m long to bring the stone from rest to 120 rev/min in 9.00 s? (b) After the grind- stone attains an angular speed of 120 rev/min, what tangential force at the end of the handle is needed to maintain a constant angular speed of 120 rev/min? (c) How much time does it take the grindstone to come from 120 rev/min to rest if it is acted on by the axle friction alone? Figure P10.58 50.0 kg m = F 160 NIn Figure, a constant horizontal force Fapp of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s?. What is the frictional force on the wheel (in N)? app Option 1 Option 2 Option 3 Option 4 Option 5 (+4.01) (-4.01) (+2.0i) (-2.01) (-5.01) a) Option5 b) Option4 c) Option1 d) Option2 abody22 e) Option3A solid, uniform disk of radius 0.250 m and mass 57.8 kg rolls down a ramp of length 4.70 m that makes an angle of 16.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/s
- A hollow cylinder, of inner radius 0.28m and outer radius 0.41m, is rotating around an axis through the center like a wheel. What would be the torque experienced if it has a mass of 4.00kg and an angular acceleration of 11.11rad/s2?A uniform solid disk of mass m = 2.95 kg and radius r= 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.98 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg · m²/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? kg - m²/sA wheel starts from rest and rotates with constant angular acceleration to reach an angular speed of 12.0 rad/s in 3.00 s. Find (a) the magnitude of the angular acceleration of the wheel and Answer 4.00 rad/s^2 (b) the angle in radi-ans through which it rotates in this time interval. Answer 18.0 rad
- An electric drill starts from rest and undergoes uniform angular acceleration for a period of 0.130 s until it turns at a rate of 2.35 x 10 rev/min. (a) What is the drill's angular acceleration (in rad/s)? (Enter the magnitude.) rad/s? (b) What is the angle (in radians) through which the drill rotates during this period? (Enter the magnitude.) radIn the construction of railroads, curvature of the track is measured in the following way. First a 100.0-ft-long chord is measured. Then the curvature is reported as the angle subtended by two radii at the endpoints of the chord. (The angle is measured by determining the angle between two tangents 100.0 ft apart; since each tangent is perpendicular to a radius, the angles are the same.) In modern railroad construction, track curvature is kept below 1.20°. What is the radius of curvature of a “1.20° curve”? answer in ft4 spheres, each of diameter D= 0.05 m (spheres are identified as 1, 2, 3, 4), are placed on the end of 4 rods of length L = 0.15 m, arranged in a cross pattern as shown in the figure. L The rigid assembly is free to pivot without friction about the axis, o, normal to the page. Sphere 1 is covered with roughness of height ɛ = 0.25 mm while all other spheres are smooth. 1 With an oncoming velocity of U= 60 m/s, which direction will the assembly rotate? (Clockwise or counterclockwise). Use appropriate calculations to explain and justify your answer. Density of air is 1.2 kg/m³ and viscosity is 1.5 x 10-5 m²/s. 3.