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 31.5° slope up 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. You currently have 25.5 kg of food left for the rest of your trip so you put 25.5 kg of rocks in the anchor bag to balance it out. What happens when you lower the food bag over the edge and let go of the anchor bag? The weight of the bags and the rope are negligible. The ice is smooth enough to be considered frictionless.
What will be the acceleration of the bags when you let go of the anchor bag?
To determine the acceleration of the bags when you let go of the anchor bag, we can analyze the forces acting on the system.
When you let go of the anchor bag, the only force acting on the bags is the gravitational force. The total mass of the system is the mass of the food bag and the mass of the anchor bag, both of which are 25.5 kg.
The gravitational force acting on the bags can be calculated using the formula:
F = m * g
Where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, we can assume g to be 9.8 m/s^2.
So, the force on both bags is:
F = 25.5 kg * 9.8 m/s^2 = 249.9 N
Since the force is equal to mass times acceleration (F = m * a), we can rearrange the equation to solve for acceleration:
a = F / m
a = 249.9 N / 25.5 kg
a = 9.79 m/s^2
Therefore, when you let go of the anchor bag, the bags will accelerate downward at approximately 9.79 m/s^2.