Work- Mechanical Energy - ‘To Do Work, Forces Must Cause Displacements’ frictionless

Ex: How much work is done by the waiter who carries a tray horizontally across the room? F v Ex: How much work is done pushing a car up an incline 10m if the incline is set at 20°? 10m F = 500N Note:FORCE IS IN SAME DIRECTION AS MOTION

Ex: A box is pulled by a rope with a force of 10N at 30 ° for 2m. How much work was done? 2m 10N “ONLY THE COMPONENT OF THE FORCE IN THE DIRECTION OF THE MOTION IS USED TO DO WORK” FxFx As the component of the force in the direction of the motion decreases, less work is done

Gravitational Potential Energy Gravitational Potential Energy – m = 100kg 2m a)How much work is done lifting the barbell? b)How much PE does the barbell have after being lifted? c)How fast will the barbell strike the ground if dropped? d)If the barbell was lifted twice as high, how much work would be the work done in terms of (W), the potential energy gained in terms of (PE), and the kinetic energy when it hits the ground in terms of (KE)?

In which situation is more work done on the ball? In which situation does the ball have greater PE? hhh A 155-newton box is pushed 5.6m up a ramp to a vertical height of 1.8m by force ‘F’. a)What is the total amount of gravitational potential energy gained by the box? b)What is the angle of the ramp? c)If the ramp has rollers and can be considered frictionless, what force is need to push the box up the ramp?

Kinetic Energy Kinetic Energy – A force of 50N is applied to pull back a.1kg arrow back.4m… a)How much work is done on the bow? b)How much KE will the arrow have when released? c)What will be the velocity of the arrow when released? d) What would be the KE if the arrow left with 2x and 3x the velocity? KE (J) v(m/s) BONUS: If the arrow was shot straight upward, how high would it go (neglecting friction)? During Flight

When work is done on a system, Energy is given to it… Mechanical Energy energy of motion stored energy Kinetic Energy Potential Energy Work-Energy Theorem: Try to trace back to the origin of the arrows KE…

Conservation of Energy (Ideal System)

A 1kg pendulum swings back and forth… a)What is the Total Mechanical Energy of the system? b)If point A is.3m above point B, how fast does the pendulum move at point B? c)If the string is cut at point B that is m above the floor, what will be the range of the projectile?

Conservation of Energy (Ideal System) – Roller Coaster

75m 20m 10m m=1000kg 5m a)Work done to get to point ‘A’? b) Force machine exerts to move the coaster 75m. c)How much PE is lost at point ‘B’? d) How much KE is gained at point ‘B’? c)How much PE is lost at point ‘B’? d) How much KE is gained at point ‘B’? e) How fast is car going at points B,C,D and E? f)What is the highest the coaster will make it up the last hill? f)What is the highest the coaster will make it up the last hill?

Graphical Representations Displacement (cm) The graph below shows the force required to compress a spring in a marble shooter. a)How much force was required to compress the spring 4cm? b) How much work was done on the spring compressing it 4cm? c)If all of the stored energy in the spring went into the KE of the 10g marble, what velocity would it have leaving the barrel? d)If the marble landed 2.2m away from the base of the table, how high is the table? e)Assuming the average force on the marble from the spring was 4N, how long does the marble acceleration in the barrel? What is the acceleration of the marble during that time?

Conservation of Energy (Non–Ideal System) a)What is the PE at 2m? b)What force was required to raise the tennis ball? c)How much Mechanical Energy (ME) was lost between point ‘A’ and point ‘B’? d)What percent of the ME was lost and where did it go? A.06kg tennis ball is dropped from a height of 2m… A 10kg crate starts from rest atop a 2m high incline and slides to the bottom. a)If the velocity of the crate at the bottom of the incline is 4m/s, much work was done by friction? b)If length ‘d’ of the incline is 5m, how much friction was present?

SPRINGS Revisited… A 1kg mass hangs from a spring stretching the spring 20cm… a) What is the restorative force of the spring? a) What is the restorative force of the spring? b) What is the spring constant of the spring? b) What is the spring constant of the spring? c) How much elastic PE is stored in the spring? c) How much elastic PE is stored in the spring? a)Which plot represents the spring with the greatest spring constant? b)Given the values, what is the value for ‘k’ of spring B? c)How much work was done on spring B? d)If the slope of D is half of B, how much force would be required stretch spring D the same as B?

Applying Conservation Laws to Springs… A 1kg mass falls for.45s before landing on a spring… a) From what height did the mass fall from? a) From what height did the mass fall from? b) How much KE does the mass have when it lands on the spring? b) How much KE does the mass have when it lands on the spring? c) If the spring has a spring constant of 50N/m, how far is the spring c) If the spring has a spring constant of 50N/m, how far is the spring compressed? compressed? d) If the spring compressed twice as far, how much energy would d) If the spring compressed twice as far, how much energy would be stored in the spring? be stored in the spring? e) If it fell from the same height, how much falling mass would e) If it fell from the same height, how much falling mass would cause the amount of stored energy from your answer to ‘d’? cause the amount of stored energy from your answer to ‘d’?

Power - 2 different people run up a flight of stairs to a height of 4m. Determine the power of each person if… a) A 50kg person makes it up the stairs in 4 seconds. a) A 50kg person makes it up the stairs in 4 seconds. b) A 100 kg person makes it up in 8 seconds. b) A 100 kg person makes it up in 8 seconds. 100W60W Power time

A horse pulls a plow with a force of 500N at a constant velocity of 2m/s… a)How much power is generated by the horse? b)How much energy does the horse use in 1s? c)How far does the horse get in 5s, and 10s? d)If 1hp = 746Watts, how many hp does the horse have? Work Power timevelocity A weightlifter lifts a 50kg mass using energy at a rate of 250J/s for 1.5s… a)How much power is dissipated by the weightlifter? b)How high does the mass rise in 1.5s? c)With what velocity does the mass rise?