How to solve for x: trig angle = X/B
SLIDE: B trig angle = x
How do you find the leg closest to the angle (adjacent to the angle) if you have the hypotenuse?
hyp * cos angle
If you are given a force and a mass, you can find ____ by using the equation ____
a = F/m
a newton (force) divided by acceleration (m/s2) will give you
mass (kg)
if force = mass * acceleration, then mass=
FORCE / ACCELERATION
How to solve for x: trig X = A/B
UNTRIG: trig-1 (A/B) = x
Diagonal force (down along the plane) is
Fd is directional, or down the plane,
parallel to the plane, along the plane
Why don’t you see the earth move when you jump up?
It is so massive that it barely moves
What is the unit of weight we use?
NEWTON
Give an example of Newton’s second law in real life:
harder to push a car than to push a skate board (mass resists acceleration, f=ma)
What are other words for “UNTRIG?”
arctrig, or inverse trig.
(arcsin, arctan, arccos or inverse sine, inverse tan or inverse cos)
Coefficients of friction are _____ for surfaces that are smooth and ____ for surfaces that are rough, or sticky.
smaller, larger
If you are given a mass and an acceleration, you can find ____ by using the equation ____
Force, F= ma
How do you sketch the net force from free body diagram?
PARALELLOGRAM RULE
Give an example of Newton’s first law in real life
an apple on a desk.
net force is zero, until you push it off (things at rest or motion stay that way)
sin 70 = cos __
20
What is Newton’s Second Law?
Force increases acceleration,
mass resists accelertion F= ma
sin 50 / cos 50 = tan ____
50
If you are given a force and an acceleration, you can find ____ by using the equation ____
mass, m= F/a
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)
What weighs 100N?
3 Gallons of milk
Where is the hypotenuse?
It is the longest side.
Always the side across from the right angle. It is the diagonal.
The force of friction always acts____
in the opposide direction of motion
What are the three equations from newton’s second law? (my fish is from massachusetts)
a=F/m F= ma F/a = m
What does the word “adjacent” mean?
It means “NEXT TO”
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.
What is the mass of an object that acceleraties 5 m/s2 when a 30N force is applied?
m= F/a
so 30/ 5 = 6kg
What weighs 1000N?
Mr. Nystrom wearing a backpack full of books
What is Newton’s First Law?
Object stays at rest, or moves at a constant velocity in a straight line unless a force acts on it.
What does SOH CAH TOA stand for?
sin angle= opp/hyp
cos angle = adj/hyp
tan angle = opp/adj
In a right triangle, the sine of one of the acute angles always equals the ____ of the other acute angle
Cosine
How much does a 3kg object weigh?
about 30N
What will the acceleration be of an 800kg car that is pushed with a force of 8000N? (ignore friction)
10m/s2
complementary angles add up to
90 degrees
Give an example of Newton’s third law in real life:
the floor is pushing up on you as much as you are pushing down on the floor (equal and opposite)
cos h = sin ____
90-h
a newton (force) divided by a mass (kg) will give you
an acceleration (m/s2)
What is a way to think of mass when it comes to movement?
MASS RESISTS ACCELERATION
this is what we call inertia
What is a NEWTON a unit for?
for FORCE and WEIGHT
weight is a force
The force between the block and the ramp is
the normal force, Fn
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)
What is the net force on an object that is moving at its terminal velocity? Explain
zero. it is not accelerating
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. This is why you don’t see the earth move.
MASS RESISTS ACCELERATION
How do you sketch the resultant force of two vectors?
USE THE PARALELLOGRAM RULE.
Do you weigh more on the ground or in an airplane?
On the ground.
The further from an object, the less its gravitational pull influences you.
sin f / cos f = tan ___
f
Give a quick summary of Newton’s three laws of motion:
FIRST: objects in motion or rest stay that way.
SECOND: harder to push more massive objects .
THIRD: action have equal opposite reactions
what are the units we use for acceleration?
m/s2
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)
What is the difference between mass and weight?
mass is the amount of stuff, mass is a measure of resistance to change, weight is the force due to gravity on the planet it is on
What weighs 1 N?
an apple
Where is the “opp” leg?
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.
What do we use normal force to calculate?
since it is the measure of the force between the block and the plane, it determines amount of friction. Friction=FN * Mu
Is acceleration scalar or vector?
vector (has direction and magnitude)
What is the net force on a 10kg object that is accelerating at 2 m/s2
F = ma so 10(2) = 20N
What receives a greater force of air resistance, an elephant or a feather falling? Why?
elephant. it is pushing through more air
What does the delta (the little triangle) symbol mean?
It means “CHANGE IN”
What is terminal velocity?
the highest speed a falling object will reach because of air resistance
Which is more stable, mass or weight? Explain
mass is same on earth or moon, weight changes on different planets with diff gravity. Also, you weigh less on a plane than on the ground (gravity decreases the further from earth you are)
How do we find the x and y components if we have the resultant?
Generally, the resultant is the hypotenuse of a right triangle. So the closest side (adjacent) to the angle can be found by HYPcos(angle) and the opposite side (across) from the known angle can be found by HYPsin(angle)
How to solve for x: trig angle = A/X
SWITCH: A/trig angle = x
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)
<p>What is the unit of force we use?</p>
NEWTON
If you have weight, how do you find normal force?
w*cos (angle) gives normal force.
What is the net force on an object moving at a constant velocity? Why?
zero (not accelerating) but has kinetic energy!
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
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 do we make sure our calculator is in the right mode?
press MODE> put cursor on DEGREES> press ENTER
a mass (kg) multiplied by an acceleration (m/s2) will give you
a newton (force)
How do you find the net force mathematically from a free body diagram?
Break the forces into X and Y.. find SUMX and SUMY, sketch, find mag with pythag and angle with tan.
<p>If you have weight, how do you find directional force?</p>
w*sin(angle) gives the directional force
SOH CAH TOA… What do these stand for?
Sin angle= opp/hyp
cos angle= adj/hyp
tan angle= opp/ adj
What is the net force on an object at rest?
zero (not accelerating), but has potential energy
What force do you need to accelerate a 1000kg car 5 m/s2 ? (ignore friction)
5000N f=ma
What weighs 10N?
Large Textbook (a 1 liter bottle of soda)
what do the two acute angles add up to in a right triangle?
90
sin m = cos ___
90-m
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.
Describe what NET force is
It is what is left after you combine all the forces (things cancel out)
angles that add to 90 degrees are called
complementary
If force = mass * acceleration, then acceleration =
FORCE / MASS
What has to be happening in order for net force to not be zero?
it must be ACCELERATING (changing velocity). just moving is not enough, it has to be changing speeds!
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)
You can calculate the force of friction by multplying ____ by ____
normal force by coefficient of friction
What are the units we use for mass?
kg
What is the mass of a 35N object?
3.5 kg
Where is the “adj” leg?
it is the close leg.
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.
When you fire a gun, the force on the bullet is equal to the _____________
force on the gun
How can we add two vectors (find resultant) by sketching?
Use the parallelogram rule, and the DIAGONAL is the resultant vector when both components start from the same spot.
block on inclined plane: What is Fd and FN?
Fd is force DIAGONAL down plane parallel along the slope, FN is normal force perpendicular to the plane between block and ramp.
What is acceleration when 12N is applied to 3kg object? Why?
4 m/s2. Since F=ma, then a=F/m
so 12N/3kg = 4m/s2
Explain Fn in plain terms
It is the squeeze force between the block and the ramp. It measures the force going directly perpendicular into the plane.
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)
cos 50 = sin __
40
What are the units in a NEWTON?
kg*m/s2 (notice it it a mass * acceleration)
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)
How to solve right triangles when there are no angles given?
PYTHAGOREAN THEOREM to find sides, then trig to find angles if you must
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!
What is Newton’s Third Law?
Every action (force) has an equal and opposite reaction
How do you find the leg furthest from the angle (opposite the angle) if you have the hypotenuse?
hyp * sin angle
Explain what Fd is in plain terms
it is the force that acts on the block pushing it down the ramp. it goes diagonally down the ramp, parallel to the ramp.
