Two 100 kg boxes are dragged along a frictionless surface with a constant accele

Question

Two 100 kg boxes are dragged along a frictionless surface with a constant acceleration of 1.06 m/s 2 , as shown in the figure. Each rope has a mass of 0.83 kg. Find the force F. Answer in units of N.

Find the tension in the leftmost rope at the point where it is attached to the leftmost box. Answer in units of N.

Find the tension in the leftmost rope at the point where it is attached to the rightmost box. Answer in units of N

Find the tension in the rightmost rope at the point where it is attached to the rightmost box. Answer in units of N.

Explanation / Answer

Treat the ropes as blocks. Draw free body diagrams of each of the four elements as follows-
For rope 1 which is 1st element from right
F-T1=ma
=F-T1=0.83*1.06
For block 1 which is 2nd element from right
T1-T2=Ma
=T1-T2=100*1.06

For rope 2 which is 3rd element from right
T2-T3=ma
=T2-T3=0.84*1.06

For block 2 which is 4th element from right
T3=Ma
=T3=100*1.06=106

=T2-T3=0.84*1.06

T2=106.9N

=T1-T2=100*1.06

=T1=212.9N

=F-T1=0.83*1.06 =213.78

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