Question

1)A block of mass m1 = 8.00 kg and a block of mass m2 = 12.0 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.350 m and mass M = 12.0 kg. The coefficient of kinetic friction between block m1 and the table is 0.27. a) Draw force diagrams of both blocks and of the pulley. b) Determine the acceleration of the two blocks. c) Determine the tensions ?1 and ?2 in the string on both sides of the pulley. d) How would the answer for ?1 and ?2 change is the pulley were massless?

2)During a certain time interval the angular position of a swinging door is described by θ = 5.3 + 7.1t + 4.5t 2 , where θ is in radians and t is in seconds. Determine (a) the angular position at t = 2 sec, (b) angular speed at t = 2 sec, and (c) angular acceleration of the door at t = 2 sec.

3)A figure skater is spinning with an angular velocity of 16 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is 5 rev. Determine (a) her average angular acceleration and (b) the time during which she comes to rest

4)A disk 6.00 cm in radius rotates at a constant rate of 98.0 rev/s about its central axis. (a) Determine the tangential speed at a point 4.00 cm from its center. (b) Determine the centripetal acceleration of a point on the rim.

5)Two girls ?1 = 21.0 kg and ?2 = 29.0 kg are standing 1.00 m away from the center of a rotation platform (Figure (a)), and the platform rotates at angular speed of 3.00 rad/s. Then both girls begin to walk towards the edge of the platform. If the radius of the platform is 2.00 m, what is the final angular speed of the system, when the girls reach the platform’s edge (Figure (b))? Model the platform as a uniform disk of mass M =350 kg, and the girls as point masses. The moment of inertia of a disk of mass M and radius R is 2 2 1 I disk = MR .

Answer 1

Solution:

1.

Given,

mass m1 = 8.00 kg, mass m2 = 12.0 kg , radius R = 0.350 m, mass M = 12.0 kg.

The coefficient of kinetic friction between block m1 and the table is 0.27

(a)

(b) The two block will move with same acceleration a.

Newtons 2nd law for mass m1:

.............(1)

Newtons 2nd law for mass m2:

...,...,.....(2)

For the pulley with moment of inertia :

  

  

.....................(3)

Rearranging eq. (1),(2)&(3).

(c)

From (1),

From (2)

(d) If the pulley were masseles, then the tensions and will be equal. There will be no torque at the pulley and tensiom will be same in the whole string.

.....(4)

......(5)

So, from(4)&(5),