You are a member of an Alpine Rescue Team and must project a box of supplies up
ID: 582954 • Letter: Y
Question
You are a member of an Alpine Rescue Team and must project a box of supplies up an incline of constant slope angle so that it reaches a stranded skier who is a vertical distance h above the bottom of the incline. The incline is slippery, but there is some friction present, with kinetic friction coefficient k.
Use the work-energy theorem to calculate the minimum speed you must give the box at the bottom of the incline so that it will reach the skier. Express your answer in terms of g, h, k, and .
Explanation / Answer
Using Energy Conservation Theorem,
Let the minimum speed needed to reach = v
Initial Kinetic Energy = 1/2mv^2
Initial Potential Energy = 0
Work done against Friction, = k m*g*cos() * h/sin()
Final Kinetic Energy = 0
Final Potential Energy = m*g*h
1/2 mv^2 + 0 - k m*g*cos() * h/sin() = m*g*h
Cancelling out m form the equation
1/2*v^2 = g*h + k*g*h*cot()
v = sqrt[2gh[1 + k*cot()]]
Minimum speed needed, v = sqrt[2gh[1 + k*cot()]]
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