Answers: (a) 177.5 N, (b) 195 N

With the box at rest, apply the 2nd Law to determine the initial tension in the top rope:

ΣF=maTt2Tbmg=maTt2(10)15(10)=0Tt=170N

When the elevator accelerates upward, the ropes undergo a slight change in length. The top rope will stretch, but the bottom ropes will contract. The length of each bottom rope decreases by the same amount that the length of the top rope increases. Given that the ropes follow Hooke’s law, the change in tension is proportional to the change in length. Accordingly, given that the ropes are identical, the increase in the tension in the top rope will equal the decrease in the tension in each...

AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.