A block with mass m1=2.00 kg rests on a frictionless table. It is connected with

Question

A block with mass m1=2.00 kg rests on a frictionless table. It is connected with a light string over a pulley to a hanging block of mass m2=4.00 kg. The pulley is a uniform disk with a  radius  of  4.00  cm  and  a  mass  of  0.500  kg.

(a)  Calculate  the  accel-eration   of   each   block and  the  tension  in  each segment   of   the   string.

(b)  How  long  does  it take the blocks to move a  distance  of  2.25  m?

(c)  What  is  the  angular speed  of  the  pulley  at this time? A block with mass m1=2.00 kg rests on a frictionless table. It is connected with a light string over a pulley to a hanging block of mass m2=4.00 kg. The pulley is a uniform disk with a  radius  of  4.00  cm  and  a  mass  of  0.500  kg.

(a)  Calculate  the  accel-eration   of   each   block and  the  tension  in  each segment   of   the   string.

(b)  How  long  does  it take the blocks to move a  distance  of  2.25  m?

(c)  What  is  the  angular speed  of  the  pulley  at this time?

Explanation / Answer

(a) drawing FBD for m2 you see that tension T = m2g = 39.2N apply this to FBD m1 we can determine the acceleration at which both masses will move using F = ma. The only force acting on m1 is T therefore 39.2N = m1*a ===> a = 19.6 m/s^2 (b) using kinematic distance equation d = 1/2*a*t^2 2.25m = 1/2(19.6m/s^s)(t^2) therefore t = 0.479s (c) to determine the angular speed we need to know the amount of degrees or radians the pulley rotated in that time. using the following equation that can be determined. arc*length = radius*theta(radians) 2.25m = 4cm*theta(radians) theta(radians) = 56.25 rad therefore angular velocity = theta(radians)/t angular velocity = 117.432 rad/s feel free to ask questions about my work.

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