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 55.5° 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 21.5 kg of food left for the rest of your trip so you put 21.5 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.
M*g = 21.5 * 9.8 = 210.7 N. = Wt. of food.
Fpd = 210.7*sin55.5 = 173.6 N. = Force parallel to the incline and downward.
sin55.5 = 210.7/Fpu. Fpu = 256 N. = Force parallel to the incline and upward.
Since the force acting up the incline is greater than that acting down the incline, the food will fall to the ground.
When you lower the food bag over the edge and let go of the anchor bag, something quite hilarious happens. Since the slope of the ice is at a 55.5° angle, which is greater than the critical angle of friction for the food bag, the food bag will start sliding down the slope. And let's not forget, the ice is frictionless, so there's no stopping it!
Now, picture this – the food bag sliding down the slope, gaining speed with each passing second. It's like watching a super-energetic squirrel on a water slide, going faster and faster. Wheeeeeee!
But, uh oh, here comes the vertical cliff! The food bag is about to experience a gravity-powered roller coaster drop! Hang on tight, little food bag. We're in for a wild ride!
As the food bag reaches the vertical cliff, it has no choice but to continue its downward trajectory. It's like a food-seeking missile, plummeting towards the ground below. And guess what? The poor bear-resistant plan didn't quite work out as intended.
So, my dear hiker, when you let go of the anchor bag, your food bag unfortunately goes on a thrilling adventure, leaving your hungry stomach behind. You might want to come up with a new plan to keep those mischievous bears away from your precious supplies!
When you lower the food bag over the edge and let go of the anchor bag, two forces come into play: the force due to gravity on the food bag and the tension force in the rope.
As the food bag hangs over the edge, it experiences a downward force due to gravity, which is equal to the weight of the food bag. Let's represent this force as W_food.
Since the ice is considered frictionless, there is no friction force acting on the food bag. Therefore, the only force acting on the food bag is the tension force in the rope. This tension force is the same as the force due to gravity and acts in the opposite direction, upwards.
According to Newton's third law, the tension force in the rope is equal in magnitude and opposite in direction to the force due to gravity on the food bag. Therefore, the tension force in the rope is also equal to W_food.
Now, since the anchor bag and the food bag are balanced, they both have the same weight. This means the force due to gravity acting on the anchor bag, W_anchor, is also equal to W_food.
When you let go of the anchor bag, since the force due to gravity on the anchor bag and the food bag are equal, and the tension force in the rope is equal to the force due to gravity on the food bag, there will be no net force acting on the system.
As a result, both bags will remain stationary in the air, hanging from the rope, without any downward or upward acceleration. They will maintain their positions, keeping your food out of reach of bears.
When you lower the food bag over the edge and let go of the anchor bag, both bags will accelerate downwards due to the force of gravity. However, since the slope forms a 55.5° angle, the force of gravity acting vertically down can be split into two components: the force pushing the bags downwards along the slope, and the force perpendicular to the slope.
The force of gravity can be split into two components: the force of gravity along the slope and the force of gravity perpendicular to the slope. The force of gravity acting along the slope will cause the bags to slide downwards, while the force of gravity perpendicular to the slope will cause the bags to press against the slope.
Since the force along the slope is greater than the force perpendicular to the slope, the bags will slide downwards along the slope. As they slide, the force of gravity along the slope will accelerate the bags, causing them to pick up speed.
It's important to note that the bags will only accelerate if there is no friction between the bags and the ice. Since you mentioned that the ice is smooth enough to be considered frictionless, the bags will continue to accelerate as they slide down the slope.
If the slope is long enough, the bags will eventually reach the vertical cliff. At this point, the bags will continue to fall vertically downwards, as the slope no longer influences their motion.