At work in Alaska you must pull two heavy boxes of supplies across a frozen lake
ID: 2047232 • Letter: A
Question
At work in Alaska you must pull two heavy boxes of supplies across a frozen lake to your camp. Fortunately there is a machine at your camp with a long cable attached that can pull the boxes for you, so you attach the cable to one box and then tie a rope between that box and the other one. The boxes are heavy, each having a mass of M = 500 kg but they are on skis that have negligible friction with the icy lake. The machine can exert any force F you like from 0 N up to 5, 000 N, but the rope will break if the tension exceeds T = 1, 000 N. When you turn the machine on you gradually raise F from 0 toward its maximum (that is what I would do, anyway), not thinking about the rope between the boxes. The general question is “what happens?” The approximations you should make are neglect friction, neglect the mass of the rope, and notice that when the rope is taut then the acceleration of the two boxes is the same.1) Set up an equation for the maximum force that the machine can exert without the rope breaking, using only the symbols F, T, and M. (Suggestion: draw a free-body diagram for the box that is being pulled by the rope. That will give a formula for the maximum acceleration of that box.)
2) Does the rope break? 3) How many boxes (if any) get across the lake?
Explanation / Answer
Use Newton's 2nd law so F total = Mass * Acceleration. If there is no acceleration then we can say F = m * a = 0 Net force must be 0... draw a free body diagram with all the forces such as mg, normal force etc. What you will get without considering Tension is that there is net force, which of course isn't true so the difference between the forces you sum up and 0 is the tension force. If from diagram you find F = 100 N downwards without considering tension, lets say, but object is not accelerating, then there is a Tension force of 100 N which is an upward force. I'm not doing all the work for you here but that will be enough to find answer.
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