The figure below shows an object of mass m1 = 1.1 kg on inclined surface. The an

Question

The figure below shows an object of mass m1 = 1.1 kg on inclined surface. The angle of the inclined surface is theta = 20 degree with the horizontal. The object m1 is connected to a second object of mass m2 = 3.55 kg on a horizontal surface below an overhang that is formed by the inclined surface. Further, an external force of magnitude F ext = 15 N is exerted on the object with mass m1. We observe both objects accelerate. Assuming the surfaces and the pulley are frictionless, and the pulley and the connecting string are massless, what is the tension in the string connecting the two objects?

Explanation / Answer

since both the objects are connected and that the surfaces are frictionless...both the blocks will have tha same acceleration... if you make a free body diagram of the objects... the 1.3 kg block will experience an mg force which will have to be split into vectors..i.e mgsin25 and the additional force of 10.73N towards the left and an mgcos25 downwards...tension to the left and the normal reaction acting upwards... for the 2.98kg block...it will experience just an mg focre downwards and the tension force upwards... so..from the 1.3kg block's free body diagram... 1.3g+10.73 - T = 1.3a ( t= tension,a= acceleration of the block) similarly...for the 2.98kg block... T - 2.98g = 2.98a now you have two simultaneous equations...solve them and get the values of 'a' and then you will get the value of the Tension in the string... i hope i could explain it properly...and hope you understand my verbal diagrams....!

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