A block with mass m=5.00kg slides down a surface inclined 36.9° to the horizontal (see the figure). The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has mass 25.0kg and moment of inertia 0.500kg-m² with respect to the axis of rotation. The string pulls without slipping at a perpendicular distance of 0.200m from the axis. How much time does it take for the block to increase its speed by 4m/s? 0 A. 1.5s B. 2.2s C. 2.7s D. 3.1s E. 3.6s 5.00 kg 36.9° 0-0-0
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- Masses m1= 8.0 kg and m2= 2.0 kg are attached at the ends of a massless rod 2.00 meters long, mounted to spin around a point 50.0 cm from one end. Calculate the rotational inertia around the mount point.A block of mass m1 = 1.55 kg and a block of mass m, = 6.25 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of 0 = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. М, R m1 (a) Draw force diagrams of both blocks and of the pulley. Choose FileNo file chosen This answer has not been graded yet. (b) Determine. the acceleration of the two blocks. (Enter the magnitude of the acceleration.) Enter a number. uation describing the angular acceleration of the pulley and the acceleration of the blocks? m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley NAn electric motor exerts a constant torque of τ=10N⋅mτ=10N⋅m on a grindstone mounted on its shaft; the moment of inertia of the grindstone is I=2.0kg⋅m2I=2.0kg⋅m2. If the system starts from rest, find the work done by the motor in 8.0 ss and the kinetic energy at the end of this time. What was the average power delivered by the motor? SOLUTION SET UP AND SOLVE We want to use W=τΔθW=τΔθ to find the total work done and then divide that by the time interval Δt=8.0sΔt=8.0s to find the average power (work per unit time). But first we need to find the total angle ΔθΔθ (in radians) through which the grindstone turns. The angular acceleration αα is constant, so we can use τ=Iατ=Iα to find αα and then apply the formulas for constant angular acceleration. The angular acceleration is α=τI=10N⋅m2.0kg⋅m2=5.0rad/s2α=τI=10N⋅m2.0kg⋅m2=5.0rad/s2 For constant angular acceleration, θ=θ0+ω0t+12αt2=0+0+12(5.0rad/s2)(8s)2=160radθ=θ0+ω0t+12αt2=0+0+12(5.0rad/s2)(8s)2=160rad The total work…
- A block with a mass of 5.00 kg slides down a surface inclined 36.9° to the horizontal Problem 2 as shown in the figure. The coefficient of kinetic friction between the block and the incline is 0.25. A string attached to the block is wrapped around a pulley on a fixed axis at O. The pulley has a mass of 25.0 kg and a moment of inertia 0.500 kg.m². The string pulls without slipping at a perpendicular distance of 0.200 m from the pulley's axis down the incline.. (a) What is the acceleration of the block down the plane? (b) What is the tension in the string? 5.00 kg 36.9°Calculate the rotational inertia of a meter stick, with mass 0.67 kg, about an axis perpendicular to the stick and located at the 39 cm mark. (Treat the stick as a thin rod.) X kg · m2A block with mass m = 5.00 kg slides down a surface inclined 36.9° to the horizontal (Figure 1). The coefficient of kinetic friction is 0.27. A string attached to the block is wrapped around a flywheel on a fixed axis at O. The flywheel has mass 11.1 kg and moment of inertia 0.500 kg - m? with respect to the axis of rotation. The string pulls without slipping at a perpendicular distance of 0.300 m from that axis. Part A What is the acceleration of the block down the plane? Express your answer in meters per second squared. ? a = 1.45 m/s? Figure 1 of 1 Part B What is the tension in the string? Express your answer in newtons. 5.00 kg ? T = 11.6 N 36.9 國
- A mass (M = 5.0 kg) is connected to a two pulley system. Pulley 1 has a moment of inertia, I = 0.5 kgm2, and a radius, R = 0.2 m. Pulley 2 has moment of inertia, I = 0.3 kgm2, and a radius, R = 0.15 m. The cord is spooled around pulley 2. The pulleys rotate about frictionless axles and the cord can be considered massless. (i) Determine the magnitude of the acceleration of m (ii) Determine the magnitude of the tension in the string attached to m (iii) Determine the magnitude of the tension between the pulleys.The circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k⎯⎯k¯ = 235 mm and has a concentric circular groove of 105-mm radius cut into it. A steady force T is applied at an angle θ to a cord wrapped around the groove as shown. If T = 59 N, θ = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration α of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration α is positive if counterclockwise, negative if clockwise; the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left..9.16 A flywheel in a motor is spinning at 570.0 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 33.0 ss, and during this time the flywheel slows down uniformly due to friction in its axle bearings. During the time the power is off, the flywheel makes 220.0 complete revolutions. At what rate is the flywheel spinning when the power comes back on? Express your answer in revolutions per minutes.
- A cylindrical metal drum, with a radius of 0.25 m, has an inertia of 11.0.kg. The drum is hollow and you may neglect the inertia of the top and bottom of the drum. The drum is free to rotate about an axle that runs through its centre and along its long axis. A cord is wrapped around the drum. The cord is pulled straight from the drum with a constant force of 60 N. As the cord unwinds, the drum rotates, with no slippage between the cord and the drum. (a) Calculate the work done by person pulling the cord as the drum rotates through 100 radians. Give your answer in Joules (b) Assuming the drum starts from rest, what is the rotational speed of the tyre after it has rotated through 100 radians? Give your answer in rad.sIn the figure, two 5.70 kg blocks are connected by a massless string over a pulley of radius 140 cm and rotational inertia 7.40 x 104 kg-m². The string does not slip on the pulley: it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 1.20 rad in 126 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T, and (d) string tension T;? Assume free-fall acceleration to be equal to 9.81 ms?. (a) Number Units (b) Number Units (c) Number Units (d) Number Units >In the figure, two 6.30 kg blocks are connected by a massless string over a pulley of radius 1.30 cm and rotational inertia 7.40 x 104 kg-m2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.800 rad in 126 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T,, and (d) string tension T,? Assume free-fall acceleration to be equal to 9.81 m/s. (a) Number Units (b) Number Units (c) Number Units (d) Number Units