Work = force(distance)
- FORCE AND DISTANCE MUST BE PARALLEL TO HAVE WORK
When determining distance, only look at the height from top to bottom. STEEPNESS DOESN'T MATTER!!!!!!!!!
STEEPNESS. DOES. NOT. MATTER.Practice problem: If a 600 N person walks up stairs that are 4m high (total height as shown in the picture below), how much work is done?
w=fd
w=(600N)(4m)
w=2400 J
If someone were to walk up 3 flights of stairs, and then later in the day go up an to the same third floor (force and distance are the same and parallel,) the person would use the same amount of work both times. If force and distance are the same and are parallel, it does not matter how the person got there, they have the same work.
Power= work/time
In order to determine power, we must first find our work and divide it by the time it to took to get that amount of work.
Power is measured in watts.
Work and Kinetic Energy
Why do airbags keep us safe?
KE=(1/2m)(v)^2
Change in KE = KE final - KE initial
Change in KE=work
Work=fd
Work=(small)f((big)d) with an airbag
Work-(big)f(small)d) without at airbag
Work airbag = Work dash
Airbags increase distance over which force is applied. Since work is the same, increasing the distance lowers the force. Less force means less injury!
KE=(1/2m)(v)^2
PE=mgh
Change in KE =work
Work, KE, and PE are all measured in Joules!
When plugging in numbers for PE, note that m is the mass, g is the gravity, and h is the height. However, mg= force which is measured in N.
Practice Problems:
1) U-Haul truck beds are 1m high. The ramp is 3m high. you are trying to load a 30N box.
a- How much work will it take to get the box from the ground into the truck
w=fd
w= (30N)(1m)
w= 30J
b- How much potential energy will the box have if it was just lifted up to the deck?
Work=PE
PE= 30J
c- How much PE will the box have at the top if it goes up the ramp?
PE=mgh
PE=30N(1m) *because the height is still 1m even though you use a ramp
PE=30J
2) You put 200J of energy into lifting a box using a pulley, but you only got out 150J of work.
a- How efficient is this machine?
efficiency= work out/work in
= 150J/200J
= 3/4 %
= 75%
b- Does this violate the conservation of energy law?
No because energy is never lost, it is converted into another form of energy such as heat.
3) A car is moving at 20 m/s speed and requires 10m to stop. How many meters will it take to stop if the speed of the car is 40 m/s?
KE=(1/2m)(v)^2
= (1/2m)(2v)^2
= 4(1/2m)(v)^2
Change in KE=work
Work=4(original)
Work= fd
4(work)=f(4d) * force is the same because of the same brake pads
Original distance= 10m
4(10m)=40m
40 M to stop the car if the speed is 40 m/s
*Raising an object twice as high gives the object twice the PE because PE=mgh so if you double the height but the force is constant, you will double the PE.
4) a 10 kg ball is on the top of a 4m ladder. If it falls off, what is the speed that the ball will have just before it hits the ground?
PE=mgh
=10kg(10m/s^2)(4m)
= 400J
KE= (1/2m)(v)^2
= (1/2)(10)(v)^2
= 5v^2
400= 5v^2
400/5 = 5v^2/5
80J= v^2
v= square root of 80 m/s
5) If you start out at the top of a roller coaster with 500 PE, what will be the PE at the bottom of the hill?
Top: PE=500J KE=0J
Bottom: PE=0J PE=500J
6) If you were to jump off of a cliff, you would start out with a maximum PE and minimum KE. As you fall, your PE decreases and KE increases until you get to the bottom where PE=0J and KE= the amount that PE started with.
Conservation of Energy
KE and PE relate in the fact that when one goes down, the other goes up, but they always equal a specific total
Example: PE =100J KE= 0J............. But when PE= 50J KE= 50J to equal out 100J when added together. This is how energy is conserved.
When a ball is about to hit the ground, the KE is at 9000J and it began with 12000J of PE. How much PE does it still have?
Total energy=KE+PE
12000J=9000J+PE
3000J=PE
Energy can never be lost!! It can, however, be transferred into another form of energy such as heat, sound, and light.
Machines
Machines are used to help carry or move an object easier. However, the work is still the same. A ramp increases the distance which decreases the amount of force needed to do the same amount of work.
work in =work out
f(d) = f(d)
Larger distance means less force needed.
Why do bolt cutters have such long handles but such short blades?
work handles = work blades
small f (big d) = big f (small d)
If you have a 4 string pulley and you pull a 1600 N weight, how much weight are you actually pulling?
work in= work out
work strings = work pulley
fd=fd
f(4m) = 1600N(1m)
f = 400 N
What is the point of using a machine if it doesn't multiply your work output?
Because it can multiply your force or distance
It is easier to push a box up a ramp opposed to picking it up because the distance is longer with decreases the amount of force needed to move the box.
You can never get more work out of a machine than you put in because that means energy would somehow be created and that is impossible.
Efficiency = work out/ work in
Efficiency can never be greater than 1 or 100&
At the beginning of this unit, I started out really understanding work and power but when we got into potential and kinetic energy, I was 100% lost and I'm sure it showed on my quiz grades. Tonight while going over past quizzes and understanding the answers, I really grasped onto the concept of KE and PE. I am kind of worried about the test because I feel like when I get all of these questions put onto assignment, I forget everything and can't figure out how to put it all together. For the most part, I believe I will be okay, I just need to remember which equation go with what types of problems.
