Rigid Body Mechanics Many other concepts which we don’t have time for Mechanics allows the invention of machines
Machines A simple machine is a mechanical device that changes the direction or magnitude of a force. 6 simple machines are the building blocks of more complicated machines The mechanical properties of a machine manage power to achieve desired forces and movement. A machine consists of a power source and actuators that generate forces and movement
Machines <ul><li>height 12 m </li></ul><ul><li>width 8 m </li></ul><ul><li>weight 50 t </li></ul><ul><li>can reach a speed of 3 km/h. </li></ul><ul><li>run by operators who operate the hydraulics </li></ul>Elephant robot (France)
Simple machine: Wheel and Axle <ul><li>Makes it easy to move things by rolling them, and reducing friction </li></ul>
Pulleys 100N ? 100N Weight suspended by pulley. How much force is required to hold the weight? What about now? Less than 100N. If angle is small, T 2 = T/2 T T 100N T 2 T 2
Pulleys Pulley systems can be to used lift heavy weights with reduced force What about work ? Raising mass against gravity changes U. Work must be the same!
Pulleys <ul><li>more energy is stored, in comparison to other bows </li></ul><ul><li>characteristic force curve "lets off" to a lower holding weight. </li></ul><ul><li>gives superior accuracy, velocity, distance compared to other bows. </li></ul><ul><li>The compound bow was first developed in 1966 by H. Wilbur Allen, a patent was granted in 1969. How old are pulleys and bows? </li></ul>Compound Bow
Levers " Give me a place to stand, and I shall move the Earth with a lever ” is a remark of Archimedes (300 BC) who formally stated the correct mathematical principle of levers. It is assumed that in ancient Egypt (5000 years ago), constructors used the lever to move and uplift obelisks weighting more than 100 tons. What’s going on here?
Levers The work to raise the load must be done (no way around it), but W = F d: we can reduce F by increasing d
Levers, pulleys, gears, and other tricks Examples of tricks to reduce force requirements are everywhere in everyday life Why do roads leading up to steep mountain wind in this way?
Problem solving A swimmer needs to cross a river as fast as possible. His speed swimming is 1.50 meters per second. The current of the river is 1.00 meters per second and the river is 15 meters wide. a. How long will it take him to swim across the river if he takes account of the current and swims so that he travels exactly perpendicular to the bank, ending up on the far bank exactly across from where he started? b. If instead he lets his body be carried downstream by the current while just aiming his body for the other bank and swimming, how long will it take to get across the river, and how far downstream from his point of starting will he end up?
Problem solving A B 1(t) - [1.5 sin( )](t) = 0 [1.5 cos( )](t) = 15 1.5 t = 15 A =(1) t = 10 B A
Problem solving Stopping distance for a car On a dry road, the coefficient of friction is about 0.8. How quickly can you slow down without slipping? I.e., what is the max acceleration which causes slowing down? Answer: Friction force is max, so 0.8g = 0.8 x 9.8 m s -2 = 7.8 m s -2 . If you are traveling at 24.6 m/s (about 80 km/h), how long will it take you to stop? How far will you travel while stopping?
Problem solving Find the normal forces acting on the sphere at points A and B. The mass of the sphere is 10.0kg