PHYS 1P21 Lecture Notes - Lecture 41: Rotational Energy, Angular Acceleration, Wrinkle

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PHYS 1P21 Full Course Notes

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Example: a 1. 2 kg block and a 1. 8 kg block are attached to the ends of a rope that hangs over a solid pulley of diameter 0. 42 m and mass 1. 3 kg. The axle of the pulley is frictionless and the rim of the pulley has enough friction so that the rope rotates the pulley without slipping. (otherwise, friction can be ignored. ) Determine the accelerations of the blocks, the tensions in the rope, and the angular acceleration of the pulley. Solution: as usual, the first step is to draw free-body diagrams. However, the new wrinkle in this problem is that we"ll also draw a free-body diagram for the pulley. Then we"ll apply newton"s second law to each block, and we"ll also apply the rotational analogue of newton"s second law to the pulley. In applying the rotational analogue of newton"s second law to the pulley, we will get an equation involving the angular acceleration.

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1. A block of mass m_1 = 2.00kgand a block of mass m_2 = 6.00 kg are connected by a masslessstirng over a pulley in the sape of a solid sik having radius R =0.250 m and mass M = 10.0 kg. These blocks are allowed to move on afixed block-wedge (what does this mean? T_1 and T_2 are equal?why?) of angle Î¸ = 30 as in figure 6. The coefficient of kineticsfriction is 0.360 for both blocks. Draw free-body diagrams of bothblocks and of the pulley. Determine (a) the acceleration of the twoblocks and (b) the tensions in the string on both sides of thepulley.

2. Two blocks, as shown in figure 5, are connected by a stringof negligible mass passing over a pulley of radius 0.250 m andmoment of inertia I. The block on the frictionless incline ismoving up with a constant acceleration of 2.00 m/s^2. (a) DetermineT1 and T2, the tensions in the two parts of the string. (b) Findthe moment of inertia of the pulley. "Step by step please".

5.17 . A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 15.0 N. (a) Draw two free-body diagrams: one for each block. (b) What is the acceleration of either block? (c) Find m. (d) How does the tension compare to the weight of the hanging block?

The masses of blocks A and B are 4.5 kg and 3.7 kg respectively.The blocks are initially at rest and are connected by a masslessstring passing over a massless, frictionless pulley. The system isreleased from rest.
a. draw a free- body diagram for each block showing all the appliedforces in the relative scale. Next to each diagram shot theexpected direction of acceleration.
b. What is the acceleration of the blocks?
c. What is the tension force in the rope?
d. how high will the 3.7 kg block move in the first 2.5 s?
e. find the speed of the 4.5 kg block at the end of 5seconds.

PHYS 1P21 Lecture Notes - Lecture 41: Rotational Energy, Angular Acceleration, Wrinkle

PHYS 1P21 Full Course Notes

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