Where is the hypotenuse?
It is the longest side. Always the side across from the right angle. It is the diagonal.
If you drag a block 20m with 5N or force, how much work did you do?
100 newton meters, or 100 JOULES
Where is the “adj” side?
if you imagine standing in a triangular room in the same corner as the angle. The adjacent side is the side you can touch that is not the hypotenuse. It makes the angle with the hypotenuse.
mv = Ft what does this say?
It is FAT MAV without the deltas
How much energy in a 4kg block traveling 3 m/s
KE = mv2/2 = 4*3^2 / 2 = 36/2 = 18 J
What does the delta triangle mean?
It means “CHANGE IN”
When you fire a gun, the force on the bullet is equal to the _____________
force on the gun
How do yu find the side furthest from the angle (opposite the angle) if you have the hypotenuse?
hyp * sin angle
How are FORCE and MOMENTUM different?
Force = mass (acceleration) where Momentum = mass (velocity). Momentum is present when an object is moving at a constant speed, Force needs acceleration to be present.
there are ______ of FORCE, ____ of WORK ,______ of POWER and _____ of ENERGY
NEWTONS of force, JOULES of work, WATTS of power and JOULES of energy
What do the interior angles of a triangle add up to?
180 degrees, since a right triangle already has a 90 degree angle, the other two angles are complementary (add to 90)
When a cannon is fired, explain how momentum is preserved.
mv(cannon) + mv(ball) before is ZERO. It has to be zero after, so the momentum the cannon moves must be opposite the momentum of the ball to cancel it out, so they must have the same magnitide. so after the cannon fires, MV (cannon) = MV (cannonball).
When you fire a gun, the momentum of the bullet just after the shot is equal to____
the momentum of the gun right after the shot.
What are the units of ENERGY?
JOULES - think of it as “work waiting to be done” or “stored work”
Which causes more impulse, a 1kg ball hitting you at 10m/s and falling, or a ball bouncing off your head and traveling back at 5 m/s?
A ball bouncing causes more of an impulse. Impulse is change in momentum. The ball that stops velocity only changes 10m/s (from 10 to 0), the bouncing ball goes from +10m/s to -5m/s, an overall change of 15m/s. The more the velocity changes, the more the momentum changes, which is a larger impulse!
How much power if you move 50 kg 20 meters in 10 seconds?
P = Fd / t = 50*20/10 = 100 WATTS
if force = mass * acceleration, then mass=
FORCE / ACCELERATION
Explain WORK units three ways
JOULE, or Nm, or kg*m2/ s2
What is the unit of work we use?
What is work?
FORCE X DISTANCE (in the direction of the applied force). Measured in JOULES
If two objects have the same velocity, the one with the larger mass has _____ momemtum
What is “FAT MAV?”
F delta T = m delta v (force * change in time = mass * change in velocity)
You lift 8kg up 5 meters, How many JOULES?
When you have sides of a triangle, but are trying to find out what an angle is, what do you have to use?
trig -1 (untrig, inverse trig, arctrig)
What is kinetic energy?
one half mass velocity squared. MOVING energy.
What types of collisions do we usually consider when solving problems in class?
We assume they are elastic collisions (similar to how we often ignore friction).
sin f / cos f = tan ___
sin 70 = cos __
How to solve triangles when there are no angles given?
If a 1 kg ball moving at 20m/s makes a 2cm dent in a wall. What was the force?
using F = m (delta v / delta t). We have m= 1kg, delta v = 20m/s- 0= 20m/s all we need is time. To find time, you need to user d = VT , or T = D/V… in this case, average velocity is (20 + 0)/2 = 10m/s .. so T = .02m/ 10m/s = .002 sec.
What are the three possible situations when solving trig ratios?
- solving for angle: trig x = A/B just untrig: X= trig-1 (A/B)
- solving for numerator: trig angle = X/B just slide the B: X= B trig angle
- solving for denominator: trig angle = A/X just switch: X = A/(trig angle)
F = ma can be changed to what?
change the a to (delta v / delta t) so you get: F = m (delta V / delta T)
this is another version of fat mav.
What is a way to think of mass when it comes to movement?
MASS RESISTS ACCELERATION (this is what we call inertia)
If you have a force and need to find the X and Y component, how do you do it?
The force given is always the hypotenuse of a right triangle. So draw an X and a Y component (a triangle). The closest (adjacent) side use FORCE * COS (ANGLE) and for the far (opposite) side use FORCE * SIN (ANGLE).
What are the two energies we talk about in this unit?
Potential (height) and Kinetic (speed)
What is an inelastic collision?
When some momentum, some energy is lost through heat, sound, etc
What are the three conservation of momentum equations we use in this class? (along with the situations
mv+mv= mv + mv (separate before and after). (m+m)v = mv + mv (stuck before). mv+mv= (m+m)v (stuck after)
How to solve for x: trig angle = X/B
SLIDE: B trig angle = x
If something is moving at a constant velocity, what do we know about force and momentum?
At constant velocity, a body is in equilibrium (all the forces cancel out). Because it is not accelerating, the net force is ZERO. But, because it is moving, there is momentum
PEo+KEo = PEf +KEf or mgh+1/2 mv2 = mgh + 1/2 mv2 (notice the mass can cancel if it doesn’t change)
If you weigh 600N and jump off of a building, do you accelerate towards the earth? Does the earth accelerate towards you?
YES, you accelerate toward the earth and YES the earth accelerates toward you (it is hard to see)
How to solve for x: trig X = A/B
UNTRIG: trig-1 (A/B) = x
If you are given the hypotenuse and need to find the side closest to the angle, how do you find it?
hyp * cos angle
What is potential energy?
mgh- non-moving stored energy. from HEIGHT.
What changes the momentum of an object?
Applying a force over an amount of time (WHICH IS IMPULSE!!). Impulse changes momentum.
If you do 20 joules of work using 5N of force, how far did you go?
WORK/FORCE=DISTANCE so 20 joules/ 5 newtons= 4 meters
If you weigh 600N and are hanging on a rope, you are pulling down 600N on the rope. The rope is pulling ______
up 600N on you!
WATTS measure ____
why does a bullet go faster forward than the gun moves backwards if they have the same force?
the gun has more mass. If you push a roller skate with the same force that you push a bus, the rollerskate will accelerate faster! Mass resists acceleration.
How is work different from energy?
WORK is being done, Energy is work waiting to be done, like a battery wating to be used.
How can you think of gravity to help you “see” objects being pulled towards eachother?
Imagine a bungee between them. A bungee between two cars may pull them both together at the same acceleration, but a bungee between a car and a skateboard will mostly pull the skateboard more. MASS RESISTS ACCELERATION
When you get the resultant X and the resultant Y, how do you find the direction (angle) of the resultant force?
angle to horizontal = tan-1 (Fy/Fx)
When do you have to use trig-1, aka UNTRIG,inverse trig, or arctrig?
when you are trying to FIND AN ANGLE (not a side)
How do you combine forces mathematically?
break the forces down into X and Y components and then combine all the X components and all the Y components into a resultant X and resultant Y. Sketch it. The diagonal of the rectangle is the resultant force and it goes in that direction.
What is impulse?
Change in momentum, or FORCE*TIME (a force over an amount of time changes momentum)
JOULES measure _____
Work and Energy
What weighs 1000N?
Mr. Nystrom wearing a backpack full of books
What is momentum?
MASS * VELOCITY
You lift 8kg up 5 meters in 4 seconds, how many WATTS of power?
You lift 8kg up 5 meters in 20 seconds, how many WATTS of power?
IF WORK=FORCExDISTANCE, then FORCE=
What are two ways to change momentum?
Change the mass or change the velocity
If you do 10 joules of work over 5 meters, how much force?
WORK/DIST= FORCE so 10 Joules/ 5 meters = 2 NEWTONs
If force = mass * acceleration, then acceleration =
FORCE / MASS
As velocity increases, momemtum _____
How to solve for x: trig angle = A/X
SWITCH: A/trig angle = x
Explain POWER units three ways
WATT or joule/s or kg*m2/s3
What is the unit of energy we use?
If you are given the hypotenuse and need to find the side opposite the angle, how do you find it?
hyp * sin angle
How do you find the side closest to the angle (adjacent to the angle) if you have the hypotenuse?
hyp * cos angle
When solving right triangles using trig, what do we do first?
LABEL THE H, the O and the A, then figure out which ratio to use, soh, cah or toa
What weighs 10N?
Large Textbook (a 1 liter bottle of soda)
What does “conservation of momentum” mean?
Momentum before = momentum after
In a right triangle, the sine of one of the acute angles always equals the ____ of the other acute angle
what are units of momentum?
massvelocity, so kgm/s
How do you sketch the resultant force of two vectors?
USE THE PARALELLOGRAM RULE.
What weighs 100N?
3 Gallons of milk
IF WORK=FORCExDISTANCE, then DISTANCE=
When you get the resultant X and the resultant Y, how do you find the magnitude of the resultant force?
use pythagorean theorem. R = sqrt (Fx^2 + Fy^2)
cos 50 = sin __
How is work different from power?
Work is force*distance, and power is an amount of work per unit of time. It is work/time. Power is a RATE OF DOING WORK, basically, how fast you can do the work.
What weighs 1 N?
What is the unit of power we use?
WATT (joule/sec) or (newton*meter/second)
What is ENERGY?
Ability to do work. Like stored work.
What is POWER? (two ways)
WORK/TIME or FORCE*DISTANC/TIME. It measures the rate of work, how fast you can do the work
sin m = cos ___
Where is the “opp” side?
If you imagine standing in a triangular room in the same corner as the angle. The opposite side is on the wall across the room from you.
EQN relating change in PE to change in KE
mg(delta h)= 1/2 m(delta v)2
What does the word “adjacent” mean?
It means “NEXT TO”
How much energy in a 25kg block 4meters high?
PE= mgh = 25104 = 1000 J
Why don’t you see the earth move when you jump up?
It is so massive that it barely moves
Explain FORCE units two ways
Newton or kg*m/s2
if two objects have the same mass, the one with less velocity has _____ momentum
What are other words for “UNTRIG?”
arctrig, or inverse trig. (arcsin, arctan, arccos or inverse sine, inverse tan or inverse cos)
What does SOH CAH TOA stand for?
sin angle= opp/hyp cos angle = adj/hyp tan angle = opp/adj
What is an elastic collision?
When all KINETIC energy is preserved (we solve problems like this, but in reality, energy is usually lost in sound and heat)
sin 50 / cos 50 = tan ____