04.4 Four blocks of mass m1=1.0 kg, m2=2.0 kg, m3=3.0 kg, and unknown mass m4 ar
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Question
04.4 Four blocks of mass m1=1.0 kg, m2=2.0 kg, m3=3.0 kg, and unknown mass m4 are on a frictionless horizontal surface as shown on the figure below. The blocks are connected by ideal massless strings. An unknown force FL is applied to the left block and is directed to the left. A known force FR=50 N is applied to the right block, and is directed to the right. The tension T12 in the string between m1 and m2 is 20 N and the tension T23 in the string between m2 and m3 is 24 N. (a) What is the acceleration of the system? (b) What is the magnitude of the unknown force FL? (c) What is the tension T34 in the string between m3 and m4? (d)What is unknown mass m4?Explanation / Answer
Let us assume that the blocks are moving in right direction and a is acceleration and m is the mass of the fourth block....so....after making the free body diagrams of each of the masses, we get the following 4 equations.... 20-FL=a........................................(1) 24-20=2a......................................(2) T-24=3a.........................................(3) 50-T=ma.........................................(4) now.....the acceleration will be 2 units....from (2) FL will be 18 N .....from(1) & (2) T will be 30 N.....from (2) & (3) and the mass of fourth block will be 10 kg......from (2) , (3) & (4)
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