If the coefficients of static and kinetic friction at A are = 0.2 and μ = 0.15, respectively, determine the angular acceleration of the spool if P = 60 N.
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- A sphere of mass 5 kg and a block of mass m2 =3 kg are connected by a light cord that passes over a pulley as shown in Figure. The radius of the pulley is R=20 cm, and the mass of the thin rim is 1 kg. The spokes of the pulley have negligible mass. The block slides on a horizontal surface. The kinetic coefficient of friction between block and horizontal surface is 0.1 Find for the linear acceleration of the two objects,John is pushing his daughter Rachel in a wheelbarrow when it is stopped by a brick 8.00 cm high (see the figure below). The handles make an angle of 0 = 20.0° with the ground. Due to the weight of Rachel and the wheelbarrow, a downward force of 407 N is exerted at the center of the wheel, which has a radius of 18.0 cm. Assume the brick remains fixed and does not slide along the ground. Also assume the force applied by John is directed exactly toward the center of the wheel. (Choose the positive x-axis to be pointing to the right.) & (a) What force (in N) must John apply along the handles to just start the wheel over the brick? 1690.53 X Your response differs from the correct answer by more than 10%. Double check your calculations. N (b) What is the force (magnitude in kN and direction in degrees clockwise from the -x-axis) that the brick exerts on the wheel just as the wheel begins to lift over the brick? magnitude KN direction ° clockwise from the -x-axisThe wheel of a car has a radius of 0.300 m. The engine ofthe car applies a torque of 240 N*m to this wheel, which does not slip against the road surface. Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a counter torque. Moreever, the car has a constatnt velocity, so this counter torque balances the applied tourque. What is the magnitude of the static frictional force?
- A car tire (hoop) has a mass of 35 kg and a radius of 0.43 m. The tire is released from rest at the top of a hill and it rolls without slipping to the bottom. “Rolls without slipping” means that the linear velocity of the center of mass is equal to the tangential velocity at the edge of the tire. Once the tire reaches the bottom of the hill it will have dropped by 10 m in vertical height. The final angular velocity ?ω of the tire at the bottom of the hill is Answer ????rads.In 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 ftA yo-yo has a rotational inertia of 950 g cm2 and a mass of 120 g. Its axle radius is 3.2 mm, and its string is 120 cm long. The yo-yo rolls from rest down to the end of the string. (a)What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed?
- An ultracentrifuge accelerates from rest to 100,000 rpm in 2.30 min. (a) What is its angular acceleration in rad/s2? _________rad/s2 (b) What is the tangential acceleration of a point 10.7 cm from the axis of rotation?_________m/s2 (d) Express this radial acceleration as a multiple of g._________gA way to test the tensile strength of a wire is to place a mass at the end of it and spin the mass with uniform circular motion. The speed at which the wire breaks is a measure of its strength. The maximum frequency of rotation before a certain wire breaks is 35.5 Hz. The wire is 50.5 cm long and has a mass of 0.656 kg. (a) Determine the speed with which the mass moves. (b) Calculate the centripetal force acting on the wireThe 12 kg disk with a radius of 650 mm is rolling while slipping under the constant force of 210 N through the handle as shown. If the wheel has mass center at a point G and the radius of Gyration is Tg rg = 300 mm, determine the linear acceleration of its mass center. The coefficient of kinetic friction between the wheel and the ground Mk = 0.28. 210 N G 15°
- the knee extensors insert on the tibia at an angle of 30 degrees (from the longitudinal axis of the tibia), at a distance of 3 cm from the axis of rotation at the knee. how much force must the knee extensors exert to produce an angular acceleration at the knee of 1 rad/s^2. given a mass of the lower leg and foot of 8.8 kg and a radius of rotation of 23 cm?A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 14 rpm in 12.0 s . Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge?The uniform disk of mass m is rotating with an angular velocity of v0 when it is placed on the floor. Determine the initial angular acceleration of the disk and the acceleration of its mass center. The coefficient of kinetic friction between the disk and the floor is μk.