Mechanics with two unkowns

bob4000

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

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Doc Al

Mentor
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 dont know how to work it out (friction is unknown)

bob4000

have drawn the diagram, but didnt really help

Doc Al

Mentor
bob4000 said:
there is friction, which is why i dont 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!

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