The lower block in the figure is pulled on by a rope with a tension force of 20

Question

The lower block in the figure is pulled on by a rope with a tension force of 20 N. The coefficient of kinetic friction between the lower block and the surface is 0.28. The coefficient of kinetic friction between the lower block and the upper block is also 0.28. (Figure 1) What is the acceleration of the 2.0 kg block? Express your answer to two significant figures and include the appropriate units An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle theta. Find an expression for the angular velocity omega in terms of g, L and angle theta. Express your answer in terms of the variables L, theta and appropriate constants. A student ties a 750 g rock to a 1.4-m-long string and swings it around her head in a horizontal circle At what angular speed, in rpm, does the string tilt down at a 10 degree angle? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Solution:

Part A) :

The tension in the ropes connecting the pulleys is T;

T= u m1g + u(m1+m2)g

= u g(2m1+m2)

here m1= 2kg block ; g= 9.8 m/s/s ; m2=1 kg ; u = 0.28

Acceleration of the block of mass 2 kg = [F- ug (2 m1 + m2 ) ]/(m1+m2)

=> a = [20 - (0.28)(9.8)* (2*2 +1) ] /(2+1)

        = [ 20 - 13.72 ] /3

        = 2.1 m/s/s

Part B)

The angular speed = sqrt [g/(Lsin theta)]

= sqrt [9.8/(1.4 sin 10) ] = 6.349 rad/s

1 rev =2pi radians (360 degrees is the angle in one complete circle)

and 1 second = 1/60 min

6.349 rad/s = 6.349 x 60/2pi rpm

                   = 60.6 rpm (revolutions per minute)

                    = 61 rpm

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