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- A force was applied to a 50 kg wheel as shown in the figure. If the wheel starts to rest without slipping Determine the angular acceleration ε, the wheel pressure on the ground N and the rotational speed of the wheel n after 10 revolutions, if the rolling friction coefficient f = 0.1. Take the radius of inertia of the wheel equal to 0.3 m.While the system shown is in equilibrium, a counter-clockwise torque T =T0sin(ωt) N-m(with T0 = 226.6 and ω=7) is applied to teh disk. What is the disk angular speed ω0 = ? in rad/s at time t = 4.2 sec? ( I = 0.2 kg.m2, b = 7.8 N-m-s/r, k = 1,504 N/m, r = 0.52m )The pendulum has a mass of 8.8 kg, a centre of gravity at G, and a radius of gyration of 0.31 m about the fixed pin support at O. At what position (in degrees) must the pendulum by released from rest so that its angular acceleration is 18.6 (clockwise) at that instant? Take = 0.25 m. The motion occurs in a vertical plane and friction is negligible. Choose the correct answer. 43.2 36.7 34.6 48.4 41.1
- A cable is wrapped around the spool’s center hub. The mass of the spool is m= 100 kg, the radius r1 = 0.4 m, r2 =0.6 m, and the radius of gyration is kG = 0.3 m. A horizontal force P = 10 N is applied to the cord. The spool is initially at rest and rolls without slipping. (2) The mass moment of inertia about point A _______(kg·m2)(two decimal places)A cable is wrapped around the spool’s center hub. The mass of the spool is m= 100 kg, the radius r1 = 0.4 m, r2 =0.6 m, and the radius of gyration is kG = 0.3 m. A horizontal force P = 10 N is applied to the cord. The spool is initially at rest and rolls without slipping. (3) The angular velocity of the spool after 2 seconds is __________rad/s (two decimal places)Q1: A cylindrical body has a mass Mand outer radius R (the moment of inertia I I= 1 2 MR^ 2 ) starts to roll from rest (upper position) down on an inclined surface. If the effect of friction force was ignored, determine the linear speed of the cylinder when it hits level ground a height h lower.
- Please answer: 3, 4, 5, 6, 8, 9, 10, 12 The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. (1) If the datum for gravitational potential energy is set as shown below, the the gravitational potential energy of the wheel at the state 1 is 0 N m(two decimal places) (ANSWER IS 0) (2) If the datum for gravitional potential energ is set as shown below, the gravitational potential energy of the wheel at the state 2 is 0 N m (two decimal places) (ANSWER IS 0) (3) At state 1, how long the spring is stretched from its unstretched state (length…A 256-lb block is released from rest when the spring is unstretched. The drum has a weight of 76 lb and a radius of gyration of kO = 0.9 ft about its center of mass O. The coefficient of stiffness of the spring is k=78 lb/ft. The radius of the drum are: rin=0.485ft and rout=0.82ft. Find the velocity of the block after it has descended d=4 feet.Consider the system of two blocks. Thereis no friction between block A and the tabletop. The mass of block B is5.00 kg. The pulley rotates about a frictionless axle, and the light ropedoesn’t slip on the pulley surface. The pulley has radius 0.200 m andmoment of inertia 1.30 kg . m2. If the pulley is rotating with an angularspeed of 8.00 rad/s after the block has descended 1.20 m, what is themass of block A?
- The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. Ignore the spring's mass. (1) If the datum for gravitational potential energy is set as shown below, the the gravitational potential energy of the wheel at the state 1 is___ N m(two decimal places) (2) If the datum for gravitional potential energ is set as shown below, the gravitational potential energy of the wheel at the state 2 is___ N m (two decimal places) (3) At state 1, how long the spring is stretched from its unstretched state (length difference):________(m) (two decimal places) (4) The…The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. Ignore the spring's mass. (5) At state 2, how long the spring is stretched from its unstretched state (length difference):________(m) (two decimal places) (6) The elastic potential energy of the spring at the state 2 is_______(N·m) (two decimal places) (7) The instantaneous center of zero velocity (IC) of the wheel at state 1 is (8) The mass moment of inertial of the wheel about its mass center G is IG =_________(kg·m2 ) (two decimal places)The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. (4) The elastic potential energy at the potion 1 is_______(N·m) (two decimal places)