WHY DO WE DO WORK? Work transfers energy from one object to another. So, what is energy? –Energy is the ability to do work. Major forms (for our purposes) –Mechanical –Thermal

THERMAL ENERGY

MECHANICAL ENERGY Kinetic Energy –Energy of Motion Potential Energy –Energy of Position

WORK-ENERGY THEOREM Work causes a change in energy: –Work done on a system can slow or speed up the object. –Work done on a system can increase or decrease the potential energy of the object (change its height).

EXAMPLE How much kinetic energy does a 1250 kg car have if it is moving at 30 m/sec? If the car applies its brakes and slows to 20 m/sec, how much kinetic energy will it have? Where did the energy go?

EXAMPLE A 105 g hockey puck is sliding across the ice at 2 m/sec. A player exerts a constant force of 4.5 N for 0.15 m in the direction to which the puck was moving. What is the new speed of the puck?

EXAMPLE A 2 kg block moving at 10 m/sec slides 15 m before stopping. What is the average force of friction? What is the coefficient of friction between the block and the surface?

POTENTIAL ENERGY

EXAMPLE You lift a bowling ball from an original position of 0.61 m to a height of 1.12 m. If the bowling ball has a mass of 7.5 kg –What was the original U? –What is the final U? –How much work was done in moving the bowling ball?

PUTTING IT ALL TOGETHER

WARM-UP

EXTERNAL VS. INTERNAL FORCES EXTERNAL FORCES Forces capable of doing work on the system (a.k.a. changing the TME of the system) –F app –F frict –F air –F tens –F norm These are called NONCONSERVATIVE forces. INTERNAL FORCES Forces not capable of doing work on the system (a.k.a. changing the TME of the system) –F grav –F spring These are called CONSERVATIVE forces.

WARM-UP

CONSERVATION OF ENERGY Now that we know the difference between external and internal forces: If no external forces are NOT doing work:

CONSERVATION OF ENERGY or

EXAMPLE Tarzan swings on a 23.8 m long vine initially inclined at an angle of 36° from the vertical. What is his speed at the bottom of the swing if he starts from rest? What is his speed at the bottom of the swing if he starts with an initial speed of 2.22 m/s? What is the tension in the vine at the bottom of the swing? If Tarzan lets go of the vine at the bottom of the swing, and the vine is 10 m above the ground how far horizontally will he travel?

EXAMPLE Nicholas is at The Noah's Ark Amusement Park and preparing to ride on The Point of No Return racing slide. At the top of the slide, Nicholas (m = 72.6 kg) is 28.5 m above the ground. Assuming negligible losses of energy between the top of the slide and his approach to the bottom of the slide (h=0 m), determine Nicholas' speed as he arrives at the bottom of the slide

EXAMPLE A roller coaster car begins at rest at height h above the ground and completes a loop along its path. In order for the car to remain on the track throughout the loop; What is the minimum value for h in terms of the radius of the loop, R? Assume frictionless. What is the speed of the car at the bottom of the loop? How many g’s do the riders experience at the bottom of the loop?