dynamics the causes of motion
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Dynamics The causes of motion. Mr. Rockensies Regents Physics. Introduction. Motion is caused by Force . Force – any push or pull on an object Symbol - F. F = ma, where F is a Force, m is a mass, and a is an acceleration. Types of Forces. Contact Forces – touch the object - PowerPoint PPT PresentationTRANSCRIPT
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DYNAMICSTHE CAUSES OF MOTIONMr. RockensiesRegents Physics
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INTRODUCTIONMotion is caused by Force.
Force – any push or pull on an object• Symbol - F
F = ma, where F is a Force, m is a mass, and a is an acceleration
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TYPES OF FORCESContact Forces – touch the object1. Normal Force (FN) –
contact force which is perpendicular to the contact surface
2. Friction Force (Ff) – contact force which is parallel to the contact surface
3. Tension (FT) – force through a rope, cable, chain, etc. can only pull
Remote Forces – act from a distance1. Gravity (Fg) – Weight2. Static Electricity (FE)3. Magnetism (FB or FM)4. Nuclear Forces
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UNITSForces are measured in Newtons,
N1 kg weighs about 10 N, 100 g
weighs 1 NRemember back to the lab we did
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Forces are vectors – have magnitude and directionJust like with projectile motion, we will need to break down resultants into its components, and find the resultant when given components.
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Mass – amount of matterWeight – force experienced by that matterMass ≠ Weight
Mass – measured on a balanceForce – measured on a scale using a spring
Equilibrium – “equal forces”, forces which are balanced or add to zero
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A breeze blowing to the east pushes a sailboat along a calm ocean with a force of 400 N. The boat has a mass of 1000 kg. What is the acceleration felt by the boat?
F = 400 Nm = 1000 kgF = ma400 N = (1000 kg)aa = 400 N/1000 kga = 0.4 m/s2
A man pushes a cart with a mass of 50 kg along an even, frictionless surface. The cart accelerates at a rate of 4 m/s2. What is the force the man pushes the cart with?m = 50 kg
a = 4 m/s2
F = maF = (50 kg)(4 m/s2)F = 200 N
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HOW DO WE DERIVE THE UNITS??
If we start with the equation, F = ma, we can replace the variables with their appropriate units.
F = (kg)(m/s2)F = kg•m = N
s2
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FORCE VECTORS
Resultant – the addition of two vectorsFor Force, we use the symbol FNET OR FR
When there is a net force, FNET, that is not equal to zero, it is said to be unbalanced. This indicates that an object is accelerating because there is a force acting on it.
When we look at the forces acting on an object, we draw them concurrently.
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Resultant vectors are found using either:a) Pythagorean Theorem + SOHCAHTOA for right
anglesb) by drawing vectors to scale for any other angles
(Like in the Combining Forces Lab (#9)
FNET
F1
F2
E
E = Equilibrant – a single force which brings about equilibrium. It is equal to the resultant but opposite in direction
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MAXIMUM RESULTANT
Forces in the same direction or zero degrees apart
7 N5 N
12 N
equals
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MINIMUM RESULTANT
Opposite direction, 180° apart
5 N 7 N•equals
2 N
Every number between 2 and 12 is a possible resultant. The equilibrant then would also be between 2 and 12, but in the opposite direction.
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ONLINE EXAMPLES
Resultant versus Equilibrant
Drawing Components
Calculate the Magnitude of the Resultant
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COMPONENTSAll forces can be resolved into horizontal and vertical components.
Case 1: Inclined Force on an object on a level surface
Fx = Fcosθ
Fy = sin θ F
Fx moves the boxFy lifts the box
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Case 2: Block on an inclined plane
FNormal
FParallel
FPerpendicular
FGravity Fparallel (F||) causes sliding
F|| = Fgsinθ
Fperpendicular(F|) = Fgcosθ
FN = F|
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PRACTICE PROBLEM 1 (PART 1)
A 50 kg sled is pulled by a boy across a smooth, icy surface. If the boy is pulling the sled 500 N at 30° above the horizontal, what is the horizontal component of the force?
sled
500 N
30°
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PRACTICE PROBLEM 1 (PART 2)
sled
500 N
What is the acceleration experienced by the sled?Does the vertical component of the force affect the acceleration?
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ANSWERSAx = AcosθFx = (500 N)cos(30°)Fx = 430 N
FNET = ma430 N = (50 kg)aa = 8.6 m/s2
The vertical component doesn’t affect acceleration. It only causes the object to lift off the ground, rather than move it backward or forward.
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PRACTICE PROBLEM 1 (PART 3)
sled
500 N
Using the same sled from the previous example, what is the weight of the sled?Find the vertical component of the force pulling the sled. Would this force cause the sled to lift of the ground? Why?
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PRACTICE PROBLEM 1 (PART 4)
sled
500 N
What is the Normal Force felt by the sled?
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ANSWERSWeight is equal to Fg. Fg = mg. Since the mass of the sled is 50 kg, we can find weight by plugging in the numbers and solving for Fg.Fg = (50 kg)(9.81 m/s2)Fg = 490 N down
Ay = AsinθFy = 500 N sin(30°)Fy = 250 N up
This would not be enough to lift the sled because the force due to gravity is much greater.
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ANSWERSThe Normal Force felt by the sled would be equal in magnitude to the Gravitational Force (Weight), but in the opposite direction (perpendicular to the surface).Therefore, FN = 490 N up
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PRACTICE PROBLEM 2 (PART 1)
A block with a mass of 100 kg is at rest on an inclined plane with an angle of 30°. What is the weight of the block?
What is the parallel force of the block?
What is the perpendicular force of the block?
100 kg
30°
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DRAWING A FORCE DIAGRAM
100 kg
30°
Green Vector represents the force due to Gravity (Weight = mg)
Blue Vectors represent the components of the weight (Perpendicular and Parallel Forces)
Red Vector represents the Normal Force of the incline pushing up on the box
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ANSWERSThe Weight of the block is equal to mass times acceleration due to gravity.W = mgW = (100 kg)(9.8 m/s2)W = 980 N
F|| = Fg sinθF|| = (980 N)sin(30°)F|| = 490 NF| = Fg cosθF| = (980 N)cos(30°)F| = 850 N
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PRACTICE PROBLEM 2 (PART 2)
What is the acceleration of the block as it slides down the inclined plane?
What is the Normal Force felt by the block?
As the angle of the inclined plane increases, what happens to the parallel and perpendicular forces?
100 kg
30°
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ANSWERS
Normal Force is equal to the Perpendicular Force, but opposite in direction.FN = 850 N
To find the acceleration of the block as it slides down the incline, we need to use the parallel force.F|| = ma490 N = (100 kg)aa = 4.9 m/s2