Q1.3 Free Fall and Types of Forces / Newton's Laws
An object is dropped from a rooftop. If upward is positive, its acceleration after leaving the hand is
-9.8 m/s^2. The acceleration towards the center of the earth is downwards (negative value), and it has a value of 9.8 m/s^2.
An object is thrown downward at 9.8m/s. If upward is positive, its acceleration after leaving the hand is
-9.8 m/s^2. Velocity and acceleration are separate, so knowing velocity does not tell you the acceleration. Once the object leaves your hand, the only thing pushing or pulling it is gravity.
An object is thrown upward at 9.8 m/s. If upward is positive, the acceleration after leaving the hand is
-9.8 m/s^2. Velocity and acceleration are separate, so knowing velocity does not tell you the acceleration. Once the object leaves your hand, the only thing pushing or pulling it is gravity.
What will be the acceleration of a rock thrown straight upward at the moment it reaches the top of its trajectory?
-9.8 m/s^2. (9.8 m/s^2 downward) Same as through out its trajectory. Lets say the rock is thrown upwards at 20m/s and we round gravity up to 10 m/s^2 to simplify this explanation. After one second, the rock is at 10m/s, then 0 m/s, then -10 m/s, then -20 m/s. The velocity changes, but the acceleration stays the same the entire time.
How is 1 N defined?
1 newton is defined as a unit of force acting on 1kilogram of mass that produces an acceleration of 1m/s^2. 1N/kg = (1kg*1m/s^2)/1kg = m/s^2
A 1-kg rock is thrown at 10m/s^2 straight upward. Neglecting air resistance, what is the net force that acts on it when it is half way to the top of its path?
10 N. Because F = mg where 1kg*9.8m/s^2 is 10 N
What will the acceleration of a rock thrown straight upward at the moment it reaches the very top of its trajectory?
10 m/s^2 downward. Neglecting air drag, the acceleration will always be the force of gravity so long as the object is in the Earth's atmosphere. The acceleration is different from the velocity
Newton's Hypothesis
17th century after Galileo Every object continues at rest or uniform motion in a straight line unless it is forced to change. Inertia: note there are different types
Snow gives his wife Serah a piggy back ride. Snow weighs 400N and Serah weighs 200N. The support force supplied by the floor must be...
600N.
Weight (Gravitational Force)
A measure of the force of gravity on an object F=mg
Scalar Quantity
A physical measurement that does not contain directional information. ex. Height, speed
vector
A quantity that has magnitude(size) and direction
If you increase the mass, what happens to acceleration? (m/s^2)
Acceleration decreases
Newton's Third Law: Why don't all forces cancel out if they're equal?
Action-reaction pairs act on different objects. Action-reaction pairs are between the same two objects. If you look at a single object, you need to calculate its net force (F_net=ma). If you look at a system (object B&A). Then the INTERNAL forces between B and A will cancel out(3rd law). If C pushes on A and it is outside the system, then it changes it. Only external forces are going to add on to the net force(2nd law).
Suzie Skydiver jumps from a high-flying plane. As she falls faster and faster through the air, how does air resistance change? Does it increase, decrease or remain unchanged?
Air resistance is greater at higher speeds.
Which will have the greatest air resistance during its fall to the ground? A feather, elephant, both will have same resistance or it is impossible to tell
An elephant. It encounters more air due to its larger size and would move faster. The feather has enough air drag present to fall to slow it down. According to Newton's Second Law, there is a net force and so the force of air drag is greatest for large and fast objects. The feather is light and it has a slow air drag with cancels each other out so it has a constant (terminal) velocity. It can't go any faster. The elephant has a huge downward weight force(mg), so even if the air drag is greater then the feather, the net force makes him accelerate downward. Since his velocity and acceleration are both in the same direction, he is speeding up downwards.
Newton's First Law of Motion (Law of Inertia)
An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Equilibrium Rule
An object is in mechanical equilibrium whenever the net force on the object is zero. The sigma stands for "the sum of". So the formula says the vector sum of all forces is equal to zero for a system in mechanical equilibrium. The downward forces are matched by upward forces. static equilibrium = zero change in force.
Air resistance and Newton's Second Law
Arrow going up represents resistance force.
Arnold Strongman and Suzie Small each pull on opposite ends of a rope in a tug-of-war. The greatest force on the rope is exerted by
Both exert the same force on the rope. So why does Suzie seem to have more force? Because of the ground friction. If Arnold was standing on ice, Suzie would be able to pull him to the center since there is less friction under Arnold's feet.
If a Mack truck (heavy vehicle) and a Volkswagen bug (light vehicle) have a head on collision which vehicle will experience the greater impact force?
Both will have the same impact force. Newton's Third law. Both the truck and the bug will feel the same force. Why would being in the heavy truck be safer? 2nd Law. With the large mass, the acceleration will be smaller versus the bug.
constant velocity
Constant speed and constant direction
Two types of force
Contact (normal force, tension, friction, air resistance) and field (gravity, electric forces, magnetic forces).
Suppose an object is being accelerated through space by a 10 N force. Suddenly the objects encounters a 10N force in the opposite direction from the first force. The object with both forces acting on it...
Continues at the speed it had when it encountered the second force. When forces cancel out, the net force becomes zero. But it being zero does not mean at the object is at rest. Since the object was already in motion, it continues at the speed it had right when it encountered the second force. No net force means no acceleration, so the speed does not change after the forces cancel out.
Field Force
Does not require contact for the force to be present. (gravity, electric forces, magnetic forces).
Newton's First Law (Law of Inertia)
Every object continues in a state of rest or of uniform speed in a straight line unless acted upon by a nonzero net force.
You know that acceleration is equal to change in velocity over time. How is acceleration produced?
F=ma or a=F/m Newton's second law of motion
There are two cars that collide into each other. Car A has less weight than Car B. Will the force exerted on each care be the same or different when they collide? F_a = F_b OR F_a > F_b OR F_a < F_b
F_a = F_b Even though car B is heavier than car A, both will experience an equal and opposite reaction (Newton's 3rd law). The reactions will be different, but the force exerted on both is the same.
Will faster or slower objects have more air resistance?
Faster objects
Newton's Third Law
For every action there is an equal and opposite reaction
Newton's Second Law (Law of acceleration)
Force equals mass times acceleration. The acceleration of an object is directly proportionate to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. F= ma OR a= F_net/m
Thrust
Force from the engine. Pushes forward
Aristotle
Greek philosopher. Mistake: "If somethings moving there has to be a reason for it (such as a force pushing)." Question is what keeps objects moving after the force is released? Such as what keeps a cannonball moving after its launched? Classified motion as natural or violent.
Magnetic Forces
Has to do with the movement of charges particles. Direction is complicated and will be discussed later in the course
Suzie Skydiver jumps from a high-flying plane. As she falls faster and faster through the air, how does her acceleration change? Does it increase, decrease or remain unchanged?
Identify the forces: The force of gravity pulling her down(W,mg,F_g). The air resistance(R) pulling her up is the upward friction force. Connect: The faster she falls the greater the air resistance becomes. The greater the air resistance, the less the net force is. A decreased net force = decreased acceleration. Answer:Her acceleration decreases as she falls faster through the air. a = F_net/m = (mg-R)/m = mg/m - R/m = g - R/m **Notice if R equals 0, then only g gravity is left, meaning free fall. a = F_net/m = (mg-R)/m = mg/m - R/m = g - 0/m = g **Notice if R equals her weight mg, then acceleration reduces to 0. a = F_net/m = (mg-R)/m = mg/m - R/m = g - mg/m = 0 0 acceleration = reaching terminal velocity, so she falls at a constant velocity.
Electric Forces
If they are opposite charges, they attract. If they are like charges, they are repulsive.
Two smooth balls of exactly the same size, one made of wood and the other iron, are dropped from a high building to the ground below. The ball to encounter the greater force of air resistance on the way down is the wooden ball, iron ball, or both will have the same air resistance
Iron ball. They are the same size but the iron would have more mass.
Will larger or smaller objects have more air resistance?
Larger objects
units for acceleration: 1N/kg = (1kg*1m/s^2)/1kg = m/s^2. So,
N/kg is interchangeable with m/s^2. Force_g = mass * gravity F_g = mg
If you place a piece of paper on top of a book and dropped them at the same time, will one of them fall faster?
No, the book being under, removes the air drag for the paper. Therefore, they should drop at the same rate.
As you stand, you are not accelerating relative to the earth. Does this mean no forces are acting on you?
No, there is a force of gravity (weight) pulling you down to the center of the earth. For there to be no acceleration, there must be an equal force upwards(the floor). The opposite forces add together to have a zero net force, so you are not accelerating.
Consider the two forces acting on the person who stands still, namely, the downward pull of gravity, and the upward support of the floor. Do these forces form an action-reaction pair?
No. These two forces are two different interactions. The floor and the person. Then the gravity with the person/earth.
GRAVITY
Objects falling due to gravity experience an acceleration that is directed toward the center of the earth and has a magnitude of 9.8 m/s^2. The velocity of an object dropped on earth increases by 9.8 m/s downward every second. v = gt velocity as a function of gravity times amount of time.
Aristotle: Violent Motion
Objects move due to pushes and pulls. Objects accelerate in the direction they are pushed/pulled. Difficulty was determining the pushing force in some cases. For example, what keeps a cannonball moving after it is shot?
Aristotle: Natural Motion
Objects will move according to their nature. Objects of "Earth" move downward and objects of "Air" move upward. Celestial Objects move in circular motion. Objects should move at speeds proportional to their weights. Discredited by Galileo
Drag
Opposite the direction of motion. Resistive forces due to fluids like liquid and gases. ex. air drag or water drag
Spring Force
Parallel to the spring or how its oriented. The spring can either pull of push depending in whether it is stretched or compressed.
Friction
Parallel to the surface of contact and opposite the direction of motion (or attempted motion)
Tension
Pull along the direction of contact with a string or rope
Contact Force
Require contact between two objects in order for the force to be present. (normal force, tension, friction, air resistance)
dynamic equilibrium
Result of diffusion where there is continuous movement of particles but no overall change in concentration. When the sum of multiple forces on a moving object is zero, that object will move at a steady speed in a straight line.
Consider the apple at rest on the table. If we call the gravitational force exerted on the apple the action, what is the reaction according to Newton's 3rd Law?
The apple pulling up on the earth. Why would the answer not be "the table pushing up on the apple?" If it was the table, both the action and reaction would be happening to the same object. The original force is the gravity
net force
The combination of all forces acting on an object or system of objects. Force is a vector quantity. See scalar and vector quantities
If you shoot a gun, what is the force of the recoil? What is the acceleration of the bullet vs the recoil on the gun.
The force exerted on the bullet is equal to the recoil due to Newton's third law. While the bullet is inside the gun, from the gun cartridge to the point right before it leaves the gun, the force is the same. The bullet's mass is small so the acceleration in greater. The mass of the gun is greater, so the acceleration is smaller.
Weight
The force with which an object presses against a supporting surface (or if suspended, in a supporting string). The weight of an object is often, although not always, due to the force of gravity weight = mass * gravity
Suzie Skydiver jumps from a high-flying plane. As she falls faster and faster through the air, how is net force affected? Does it increase, decrease or remain unchanged?
The greater the velocity, the less the net force is.
Suppose two carts, one twice as massive as the other, fly apart when the compressed spring that joins them is released. How fast does the heavier cart roll compared to the lighter cart?
The lighter cart moves twice as fast. Since they both experienced the same force, the one with the smaller mass will have a bigger acceleration.
Two identical spring-loaded dart guns are simultaneously fired straight downward. One fires a regular dart; the other a weighted dart. Which dart hits the ground first?
The regular dart. Since the dart gun pushes the same force on the darts and the masses are different, the object with the smaller mass will have a greater acceleration, and therefore hit the ground first. For ex, it is easier to move a paper clip then an elephant due to the weight.
3rd Law: A rock falling under the influence of gravity. If action is considered to be that on the Earth pulling down on the rock, can you clearly identify the reaction force?
The rock pulling up on the earth
Inertia
The tendency of an object to resist a change in motion.
Kinematic Equations
Use to solve problems in one dimension with uniform acceleration (free-fall). Equations which arise from the definition of velocity. They relate the position of the cg to velocity components. Cg being centre of gravity. *(No x) V_f = V_i + at t = (v_f-v_i)/a *(No v_f) delta x = v_i*t + 1/2at^2 *(No t) V_f^2 = V_i^2 + 2a(x_f - x_i) V_f^2 = V_i^2 + 2a(delta x) *(No a) delta x = 1/2(v_o+v_f)t *(No v_i) delta x = v_f*t - 1/2at^2 x= displacement, v_f= final velocity, v_i = initial velocity, t= time, a= acceleration V_i is sometimes shown as V_o *How to solve? Define the unknown and the three knowns. usually, a = 9.8m/s^2 acceleration of gravity. v_i = 0 if the object was originally at rest and the third known variable depends on what is given in the problem Find the right equation and solve for the unknown.
Galileo
Used a ramp and dropped a ball down one ramp to see how it goes up the second ramp. Found that no matter how steep the 2nd ramp was, the final position of the ball matched the height of the initial position. If the second ramp was flat, the ball would keep going without slowing down: inertia. 2000years after Aristotle, Early 17th century. Dropped stones of different weights from the Leaning Tower of Pisa to test Aristotle's hypothesis. Observation: with only small deviation due to air drag, both objects fell at same rate. Discredited Aris's theory of natural motion: Objects do not move at speeds proportional to their weight.
Force
Vector quantity of push or pull. m/s^2
Weight as a force of gravity
W = mg, where g= 9.8 m/s^2
Velocity vs. Acceleration
When acceleration is in the same direction as velocity, the object moves faster. When acceleration is in the opposite direction as velocity, the object slows down. When acceleration is perpendicular to the velocity, the object changes direction of movement. When acceleration is zero, the object moves at constant velocity.
mechanical eqilibrium
When no force is exerted on the object
F=ma to F_g=mg
When the net force on an object of mass m is only the force of gravity, acceleration is only the force of gravity. a is expressed as g only when gravitational force acts on an object. F_g = mg = W aka. the weight of the object.
Newton's Third Law (Law of action and reaction)
Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first You can't touch without being touched. Distinguish force acting on and force exerted on, then identify the system involved. Every action (force) has an equal and opposite reaction (force). Forces can be described as the interaction between two objects. Object A pushes on object B and object B pushes on object A.
A woman holds a book stationary against the wall. Friction on the book by the wall acts upwards, downwards, or you can't say?
You can't say. We don't know if the book is heavy or not, so we don't know which way it would try to move if the woman is heavy or light. We would have to know which is larger to make an inference.
parallelogram rule
a method for adding vectors graphically. Draw a vertical dotted line going through the middle (resultant of the vector pair) and dotted lines parallel to the ropes. If the girl is 300 N, the resultant would be 300 N up dues to gravity. Then the forces cancel each other out to 0 N, so the girl is in equilibrium. When the ropes are 60degrees from the vertical, the angle between the rope is 120degrees. So, in this case, the tension of each rope is 300 N and the vertical is also 300 N. If the rope forms different angles, the parallelogram forms different shapes. So tension could be greater in the shorter rope since it is closer to the middle vector. Rope tensions can be greater then the rope they support when the angles to the vertical go beyond 60degrees
Vector Quantity
a quantity that has both magnitude and direction. ex. Moving North at 6mph
Newton scale
a weighing scale that works in opposition to the pull of gravity by measuring the upward pull needed for object to reach equilibrium; this upward force is reported as the object's weight. 1kg = 10Newtons
Normal Force
always perpendicular and away from any surface of contact. ex. an object on a wall or table
The distance traveled by an object dropped on earth can be calculated
d = 1/2 gt^2 every second the speed increases, so the distance increases as well
As a woman falls faster and faster through the air, the magnitude of her acceleration
decrease. As she picks up speed, her air drag will increase cancelling more of her weight force.
When all forces are balanced and the net force is zero, the object is said to be in...
equilibrium. It does not accelerate (change its motion). It will either continue to stay at rest or continue at the same speed in a straight path.
Galileo's hypothesis
if there is no interference with a moving object, it will keep moving in a straight line forever. Testing: rolling balls on inclined planes. Balls rolling down hills speed up and balls rolling up a hill slow down. Conclusion: In the absence of friction, the ball will roll until it reaches the same initial. In the absence of friction, the ball would move forever on a straight surface. Aristotle did not consider friction in his theory.
Acceleration is inversely proportionate to
mass. The greater the mass, the less you can accelerate since there is more inertia to overcome. The more the mass, the more the inertia. a~1/m
Different ways weight can be written
mg, F_net, W
Acceleration is directly proportional to the
net force. The greater the force, the greater the acceleration. The direction of acceleration is ALWAYS in the direction of net force. a~F_net
Mass
quantity of matter in an object. It is also the measure of inertia or sluggishness that an object exhibits in response to any efforts to start it, stop it, or change its motion in any way. weight = mass * gravity mg = ma, so a = g
Motional Inertia
resistance of a body to changes in motion.
Air drag or air resistance depends on
size and speed
When an object is first dropped, it has no
speed and thus resistive force. As it begins to fall, its speed increases, and so does the resistive force. As a result, the magnitude of the acceleration with which it falls decreases. Eventually the falling object reaches a speed high enough for the resistive force to be equal in magnitude to the weight. At this point, acceleration is zero and speed becomes constant. Then your net force is 0, so acceleration is 0. For the remainder of the fall the object descends at constant velocity.
Weight
the Force due to gravity. It is directed toward the center of the Earth or the object pulling on it.
Mass
the amount of matter in an object
terminal velocity
the constant velocity of a falling object when the force of air resistance is equal in magnitude and opposite in direction to the force of gravity(acceleration)
What is terminal velocity
the constant velocity of a falling object when the force of air resistance is equal in magnitude and opposite in direction to the force of gravity. When there is no acceleration due to air upward & downward forces cancelling out.
Support force / Normal force
the upward force that balances the weight of an object on a surface
If you have a net force
you have an acceleration