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kamalpreet122
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Homework Statement
On a cold day, a 35kg child takes a 3.5 kg toboggan to a snowy hill to slide down it. There is Us = 0.15 and Uk=0.05 between the hill and the toboggan. What is the minimum incline required before the toboggan will slide? What angle is required for the child to accelerate at half the rate of gravity?
The Attempt at a Solution
Given:
Us (coefficient of static friction) = 0.15
Uk (coefficient of kinematic friction) = 0.05
Ff (force of friction) = -X-component of Weight (mg)
Fn (normal force) = - Y-component of weight (mg)
therefore...
Ff = -mgCos[tex]\theta[/tex]-------- 1
Fn = -mgSin[tex]\theta[/tex]-------- 2
From equation 1
mg = - Ff / Cos[tex]\theta[/tex] ----- 3
Sub in 3 into 2
Fn = - (-Ff/Cos[tex]\theta[/tex] )( Sin[tex]\theta[/tex] )
Fn = FfTan[tex]\theta[/tex]
Minimum angle required for the object to slide is Critical Angle.. (therefore theta now represents critical angle)
--> Fn= FfTan[tex]\theta[/tex] ------ 4
Ff = UsFn ---------5
Sub in 5 into 4
Fn = UsFnTan[tex]\theta[/tex]
Fn / UsFn = Tan[tex]\theta[/tex]
Tan[tex]\theta[/tex] = 1 / Us
Tan[tex]\theta[/tex] = 1 / 0.15
-----> Tan[tex]\theta[/tex] = 6.67
[tex]\theta[/tex] = Tan-1(6.67)
[tex]\theta[/tex] = 81.5
So therefore 81.5 degrees is the minimum incline required for the toboggan to slide.. I think that's the answer to the first part of this problem.. I am not too sure though because I'm in grade 11 and haven't been taught much about such types of problems. Can someone please help me do the second part and check if i did the first part right.. i would really really appreciate it.
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