Forces
As we discussed forces (particularly balanced ones) in class we create a method for approaching these problems. It begins with a force picture (sketch) of the forces acting on some object of interest. We first seek to identify any "magic" forces (those that don't require physical contact between objects such as gravity and magnets) and then we know that any remaining forces must result from a physical contact (touching) with some other object. In each of these problems be sure to start by making a force picture. Remember to check your units in each calculation and refer to class discussions for the definition of N (Newtons) as well as the force due to gravity.
1) Let's start with an apparently straight forward situation. You are standing confidently on the floor. We'll assume that you're an average human being with a mass of 65 kg. Sketch the forces acting on you and determine the force that the floor is exerting on the bottom of your feet (in Newtons). Is there a fiction force on your feet when you're standing still?
2) Now imagine a stack of 4 people standing on each other's shoulders. The bottom person has a mass of 90 kg, the next has a mass of 80 kg, then 70 kg, and finally 60 kg. Sketch the forces on the 80 kg person (be sure you only have 3 and determine the force on that person's feet and the force on their shoulders. I'm trying to get you to be careful about contact and non-contact forces. You will need to remember our discussion about the fairness of the universe in the sense that when I push on you, you push back with the same force:)
3) ...and then there's the question about elevators. Assuming that everyone has played in an elevator at some point in their life you know that there are variety of different experiences that you have. Problem 1 above describes what you feel when you are standing in the elevator waiting for it to start. Does your force picture change as you are riding up in the elevator between floors? Think about what it feels like while you are moving smoothly between the floors (not at start up or stopping). What is the force on your feet (which is what you feel) under these circumstances?
4) Now consider that moment when the elevator is just starting up. What do you feel? Do you feel heavier or lighter? What is this telling you about the force the floor is putting on you? Does your force picture change for this setting? Do you think the force from the floor is bigger or smaller than the force of gravity on you at this moment?
5) In class we explored the force needed to hold a length of chain up off the floor. The expression we created was Fup=λ.L.g where λ is the linear mass density in kg.m (or g/cm), L is the length of the chain off the desk, and g is the magic conversion constant for gravity which is 10 m/s2. Let's do similar calculations for gold chain (just for fun) The linear mass density for 6 mm gold rope chains is roughly 1 g/cm. The force that will break this chain is 550 N. How long a piece of chain can I pick up before the chain will break under it's own "weight"? For those who are amused by such things here is the link to the study of breaking strength for various gold chains by a someone in the jewelery industry.
6) As we talked about in class, the idea of a space elevator is very intriguing. The current challenge is that steel cable breaks under it's own weight before it's anywhere near long enough to make a cable into space. Heavy wire rope (1 inch = 2.54 cm) has a linear density of 6 kg/m and a breaking force of 0.47 MN (mega-Newtons not Minnesotas). How long will such a cable be when it breaks under it's own weight? How does this compare to the 36,000 km needed to reach the magic geosynchronus orbit?
7) Now lets talk about the physics challenge my colleague offered the students in North Carolina. For a typical tube the linear density of the water inside is about 75 g/m (or 0.075 kg/m). If the force of the water pushing up on the bottom of the water in the tube (it's a big straw) is 7.5 N what is the maximum height (in m) that the water can be lifted up the tube if you suck all of the air out of the tube (even if that were possible)?
