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It is better to work in the pulley's frame of reference. The acceleration of pulley can be found out by a = F/(ma+mb) This acceleration is in upward direction. Therefore a pseudo force will act on both the masses in the downward direction. We can now draw their free body diagram|dw:1370323598869:dw| Be extremely careful to note that a' is the acceleration of ma and mb in the pulley frame of system and NOT the inertial frame which is the ground. We can write equation of motion for both masses and solve for a' and T. Now we have to find aA and aB which are their acceleration in the ground frame of reference. Now the entire system is going upwards with "a". Mass a is moving upward with "a" and downwards with "a' " So its total downward acceleration will be = aA = a' - a Mass b is moving upwards with "a" and upwards with "a' " So its total upwards acceleration will be = aB = a' + a
didn't get it, can you be more specific please?
Do you know what "pseudo force" is ? Because you cannot solve it without knowing that.
i'm quite confused, which blocks behaves in what way
When we want to apply equation of motions to any object in an accelerated frame of reference ,we have to apply an additional force to that object called"pseudo force". And the direction of pseudo force is opposite to the direction of acceleration of the frame in which we are working. For eg : In a train which is accelerating forward, a box on the floor will try to go backwards. It is as if the box is being applied a force in the backward direction. Is this much clear?
Yes , we are trying to measure the effect of inertia by using pseudo force.
The pulley is being accelerated upwards , so pseudo force will act on every object we are trying to study in downwards direction. After all ,the blocks will want to stay downwards. The measure of pseudo force on a mass,m is given by: Pseudo force = m * acceleration of the frame.
sorry, i didn't understand. Anyways, thank you so much, you sacrificed so much time
Let me take a particular value of F. Perhaps that will clear things up Suppose F=124N The acceleration of the entire system will be given by Newton's 2nd law a=124/M where M is mass of system. Since pulley and ropes are massless, the total mass is the mass of blocks which is 10+20 = 30kg So, a= 124/30 = 4.13m/s2 Let acceleration of blocks' in pulley system be a'. Now in addition to weights and tension, a pseudo force will also act on the blocks and the measure of pseudo force will be = m * a where m is the mass of any block and a is acceleration of system found above and it will be downwards since pulley is accelerating upwards. Now consider the free body diagram i drew before. Equation of motion of mass, mA mA*a+mA*g - T = mA* a' For mass mB T- mB*g - mB *a = mB*a' Adding these two equations and using a= 4.13, we get a' = 4.71 m /s2 Now ,we see from the figure that in pulley's frame mA is going downwards with a' but the pulley itself is going upwards with a So, its net downwards acceleration will be = a-a' = 0.58 m/s2 mB is going upwards in pulleys frame with a and the pulley itself is going with a' acceleration. So, its net upward acceleration will be a+a' =8.84 m/s2
a) T = 62N , aA = a2 = 0 m/s2 , b) T = 147 N, aA = 0 m/s2, aB = 4.89 m/s2 , c) T = 212 N, aA = 0.800 m/s2, aB = 11.4 m/s2