Internal vs External Forces Internal Forces External Forces

Internal vs. External Forces Internal Forces External Forces • Fgrav • Fspring • • • Fapp Ffrict Fair Ftens Fnorm

Internal Forces • When work is done by an internal force total mechanical energy (KE & PE) is conserved. – The sum of KE and PE remains Constant

External Forces • When work is done by an external force total mechanical energy (KE & PE) is changed. • If work is positive the object gains energy – Force and displacement are in the same direction • If work is negative the object loses energy – Force and displacement are in the opposite direction • Energy gain/loss can be in the form of PE, KE, or Both • “Non conservative forces” • Only if external Force has a vertical component can it contribute to PE change

Relating Work to Energy • Total mechanical energy plus work done by external forces is equal to the final total mechanical energy. TMEi + Wext = TMEf or KEi + PEi + Wext = Kef + PEf

Example Problem

Example Problem

Example Problem

A 1000 -kg car traveling with a speed of 25 m/s skids to a stop. The car experiences an 8000 N force of friction. Determine the stopping distance of the car.

At the end of the Shock Wave roller coaster ride, the 6000 -kg train of cars (includes passengers) is slowed from a speed of 20 m/s to a speed of 5 m/s over a distance of 20 meters. Determine the braking force required to slow the train of cars by this amount.

A shopping cart full of groceries is sitting at the top of a 2. 0 -m hill. The cart begins to roll until it hits a stump at the bottom of the hill. Upon impact, a 0. 25 -kg can of peaches flies horizontally out of the shopping cart and hits a parked car with an average force of 500 N. How deep a dent is made in the car (i. e. , over what distance does the 500 N force act upon the can of peaches before bringing it to a stop)?

Stopping Distance • Force that does work over a distance to remove mechanical energy from an object. TMEi + Wext = TMEf Then stopping is KEi + Wext= 0 J Then. 5*m*v 2 + F*d*cos 180= 0 J Therefore. 5*m*v 2 = F*d And v 2 α d stopping distance depends on velocity squared If velocity doubles, distance quadruples

Mechanical Energy Conserved • If only internal forces are doing work then there is no change in TME, therefore: KEi + PEi = KEf + Pef • PE increases KE decreases (& vice versa) • PE is transformed into KE (& vice versa) • TME is conserved

Pendulum Motion • What forces act upon a pendulum that is swinging? (hint one is internal the other is external) • Is the external force doing work? • Is energy conserved? • What happens to PE and KE as height decreases? • Where do you expect the pendulum to have the greatest PE? (A, B, or C) • Where do you expect the pendulum to have the greatest KE? (A, B, or C) WARNING: PLEASE IGNORE AIR RESISTANCE & FRICTION

TME Conserved Systems • Roller Coasters • Ski Jumpers