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 outcropping forms a slope of angle θup to a vertical cliff. You decide that this is an ideal place to hang your 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 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 will be the acceleration aof the food bag when you let go of the anchor bag? Assume that the weight of the rope is negligible, and that the ice can be considered frictionless.Express the resulting acceleration aof the food bag in terms of θ and g, the acceleration due to gravity. Let the positive direction for this bag be downwards.

Answer 1

Answer: the acceleration is (g( 1 - sinθ)) / 2

Explanation:

the tension in one bag is expressed as;

T = ma + mg sin θ ........................lets say equ 1

now the tension in another bag is expressed as;

T = -ma + mg..................lets say equ 2

so equate both equations

ma + mg sinθ = -ma + mg

2ma =  mg ( 1 - sinθ)

a = (g( 1 - sinθ)) / 2

therefore the acceleration is (g( 1 - sinθ)) / 2