As a hiker in Glacier National Park, you are looking for a way to keep the bears

Question

As a hiker in Glacier National Park, you are looking for a way to keep the bears from getting at your supply of food. You find a campground that is near an outcropping of ice from one of the glaciers. Part of the ice food supply, as the cliff is too tall for a bear to reach it. You put all of your food into a burlap sack, tie an I place to hang your unstretchable rope to the sack, and tie another bag full of rocks to the other end of the rope to act as an anchor. The mass of rocks that you put into the anchor bag is equal to the mass of food in the other bag. What happens when you lower the food bag over the edge and let go of the rope? Assume that the weight of the rope is negligible, and that the ice can be considered frictionless. Express the resulting acceleration of the food bag in terms of and g, the acceleration due to gravity. Let the positive direction for this bag be downwards a=

Explanation / Answer

let m1 is the mass of the food and

m2 be the mass of th bag

T be the tension in the rope

net force of m1 is m1a = m1g -T

also m2 is the weight can be resolved into two compoenents

m2 cos theta and m2g sin theta

so net force of m2

m2a = T - m2 g

solving above two equations

m1g - m1a = m2 a + m2 g sin theta

accleration

a = g(m1- m2 sin theta)/(m2+m1)

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