Pulley Problem: An object of mass mi (25 kg) sits on a horizontal frictionless t

Question

Pulley Problem: An object of mass mi (25 kg) sits on a horizontal frictionless table. The rope attached to it runs horizontally to a pulley and down to a hanging mass m2 (20 kg). my O (Please use the x and y directions shown to answer the questions below.) a.) Find the acceleration of each mass, and the size of the tension in the rope: (Note: Make sure to find the general expressions first; this is an extremely important skill. Only after that, plug in the numerical values.) m/s ay T= (Is it less, the same, or more than the weight of the hanging mass? Does this make sense?)

Explanation / Answer

a] let tension be T

T = m1a

also m2g - T = m2a

a = g*m2/[m1+m2]

= 9.8*20/[20+25] = 4.3556 m/s^2

T = m1*a = 25*4.3556 = 108.9 N

a1x = 4.3556 m/s^2 , a1y = 0

a2x = 0 , a2y = - 4.3556 m/s^2

b] a = m2*g/[0+m2] = g = 9.8m/s^2

a2x = 0 , a2y = - 9.8 m/s^2

c] a = 0*g/[0+m1] = 0 m/s^2

a1x = 0 , a1y = 0

d] No, not possible because tension is the only force acting on m1. We found this by our acceleration equation a = m2g/[m1+m2].

If it is not frictionless, then it is possible because friction can negate tension.

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