How to Calculate Tension in a Rope on an Inclined Surface with Two Unknowns

[bob4000]

dear reader

i have this query which i have not been able to tackle, even after many attempts. i have also consulted my teacher but to no avail. (by the way, this is not actually homework, just work i decided to do).

a toboggan of mass 20kg is pulled, with rope, up a snow-covered hill inclined at 15deg to the horizontal. the rope is inclined at 30 deg to the horizontal. explain why the tension in the rope must certainly be greater than 52.5N. could you please show step-by-step instructions with an answer preferably, just so i know how to apply this technique in the future. thank you

 

[Doc Al]

Our policy here is for you to do the work! But we'll be glad to help.

Hint: Consider the forces parallel to the hill. Include the components of rope tension and the toboggan's weight. (I assume there is no friction.)

Give it a try. (Why do you say "two unknowns" in the title?)

 

[FredGarvin]

With problems like this I always make my coordinate system parallel with the incline. For me that seems to help. Perhaps you too.

Draw a free body diagram before you do anything. Like DocAl mentioned, there are not two unknowns in this problem.

 

[bob4000]

there is friction, which is why i don't know how to work it out (friction is unknown)

 

[bob4000]

have drawn the diagram, but didnt really help

 

[Doc Al]

there is friction, which is why i don't know how to work it out (friction is unknown)

Well you can always ignore the friction. See what the minimum tension is without friction... maybe that's all you need. (Friction will just add to the tension.)

So... ignoring friction, what forces act on the toboggan? And what are the components parallel to the slope?

 

[bob4000]

thanks to all who contributed. keep up the good work

 

[FredGarvin]

If my FBD is correct, the force required without friction is higher than the limit posted.

You didn't mention anything about friction in the original question!