Journal 9/30/13

1. Journal 9/30/13 Imagine you pull really hard on a rope and it snaps. Why does it snap? What’s going on with the forces at the place it snaps? Objective Tonight’s Homework To learn about tension, another special force Finish the practice problems.

2. Notes on Pulleys and Tension Tension as a Force Our next special force to discuss is tension. Tension is a force created by ropes, chains, and other flexible objects. Tension always opposes other forces; it never acts alone. Let’s look at a simple tension setup to see how this force works.

3. Notes on Pulleys and Tension Here we have a block hanging from a rope tied to a ceiling. Gravity pulls down on the block.However, since the block isn’tmoving down, we know there’san equal and opposite forcepointing up. This is the forceof tension. But how does this force work? Let’s go conceptual for a moment and look at our rope up close. FT Fg

4. Notes on Pulleys and Tension Up close, a rope under tensionis actually made of millions oftiny pairs of opposite and equalforces. = All of these forces cancel, sowe can simplify everything downto just one pair of forces that cancel out. This simplifies things so that we have just one forcewe call “tension” instead of the millions that actually exist.So why mention the millions of forces? If we have a weak spot in a rope or chain, the opposite tension forces at that point can exceed what it can handle, snapping the rope or chain.

5. Notes on Pulleys and Tension Fixed Pulleys A pulley is a wheel through which we can loop a rope.They allow us to change the direction or strength of a tension force without changing any other properties. For the purposes of this class, we’ll assume that all pulleys have zero friction. A fixed pulley is one that is attached to a wall or ceiling and cannot move. Ropes going through fixed pulleys will have the direction of forces changed but nothing else.

6. Notes on Pulleys and Tension Fixed Pulley Example A man is pulling down on a pulley with a barrel at the other end. Ifthe barrel weighs 50 kg, how hardwill the man have to pull to haulthe barrel up?

7. Notes on Pulleys and Tension Fixed Pulley Example A man is pulling down on a pulley with a barrel at the other end. Ifthe barrel weighs 50 kg, how hardwill the man have to pull to haulthe barrel up? Gravity pulls down on the barrelfrom one end. This force is:F = ma F = (50 kg)(-9.8 m/s2) F = 490 NThis means our man needs to pull with at least 490 N of force to get the barrel moving. same FT FT Fg

8. Notes on Pulleys and Tension In this example, the man can pullthe rope in any direction. Nomatter which way he pulls, it willcreate a tension force going upward on the side of the ropewith the barrel. same FT FT Fg

9. Notes on Pulleys and Tension Moveable Pulleys If we detach our pulley so it canmove with the rest of the rig, itchanges things. We now have 2 tension forces, one on each side of the pulley.What this means is you can nowpull the object higher with only half the force, since the other half is on the other end of the pulley. Note that any fixed pulleys we have will not reduce force, just change direction. FT #2 FT #1 Fg

10. Notes on Pulleys and Tension But wait! It seems like we’regetting somethingfor nothinghere since this lets us pull anobject up without having to workas hard! The tradeoff here comes in distance. If I want to raisethe object 1 meter, I’ll actuallyneed to pull out 2 meters of rope. On the diagram at right, you can seethat if the weight rises by 1 meter, we’ve shortened 2 sections of rope by 1 meter as well, for a total of 2 meters of rope. 1m 1m

11. Notes on Pulleys and Tension Moveable Pulley Example If the load exerts a downwardforce of 300 N, what force will we need to pull with to raise it? 300 N

12. Notes on Pulleys and Tension Moveable Pulley Example If the load exerts a downwardforce of 300 N, what force will we need to pull with to raise it? The hanging pulley splits the forceso each red segment has 150 Nof force. The upper pulley is fixed, so it justchanges direction. This leaves uswith a pulling force of 150 N. 300 N

13. Notes on Pulleys and Tension Moveable Pulley Example 2 If the load exerts a downwardforce of 300 N, what force will we need to pull with to raise it? 300 N

14. Notes on Pulleys and Tension Moveable Pulley Example 2 If the load exerts a downwardforce of 300 N, what force will we need to pull with to raise it? Start at the weight.Each red line splits the 300 N in two, so each red is 150 N. Each orange line splits again, sothe orange lines are 75 N each. We split again for green to 37.5 N. And again for blue to 18.75 N. That’s our final force! 300 N

15. Notes on Pulleys and Tension Harder Problems We can combine pulleys with anything we’ve done so far. Blocks being pulled off tables by a pulley attached to something off the edge, multiple forces in each direction, etc. When dealing with pulley problems, just remember that fixed pulleys change direction of forces and moveable pulleys split forces in half. All forces coming from a weight are split evenly. Otherwise these problems are just like ones we’ve done before.

16. Practice You have the rest of class to practice the below. If you don’t finish, this will be for homework. 45 N 12 N 38N 12 N 18 N 32 N 450N 60 N

17. Exit Question #16 Imagine a chain with a weak link. If enough force is placed on the chain it will snap at the weak link. This is because… a) The forces are stronger at that point b) That link can’t withstand the same force the rest of the chain can c) That link will experience twice the force of any other link d) The chain WON’T snap at that point. It’ll snap at one of the ends. e) The chain WON’T snap at that point. It’ll snap in the exact middle. f) None of the above are right.