Exam 2
An apple weighs 1 N. When held at rest above your head, the net force on the apple is
0
A falling skydiver of mass 100 kg experiences 500 N air resistance. The acceleration of the skydiver is
0.5 g
An apple at rest weighs 1 N. The net force on the apple when it is in free fall is
1 N
distance=
1/2 x a x t^2
It takes 40 J to push a large box 4 m across a floor. Assuming the push is in the same direction as the move, what is the magnitude of the force on the box?
10 N
A tow truck exerts a force of 3000 N on a car, accelerating it at 2 meters per second per second. What is the mass of the car?
1500 kg
A car moves 4 times as fast as another identical car. Compared to the slower car, the faster car has
16 times the KE.
A car moving at 50 km/hr skids 20 m with locked brakes. How far will the car skid with locked brakes if it were traveling at 150 km/hr?
180 m
A jumbo jet has a mass of 100,000 kg. The thrust for each of its four engines is 50,000 N. What is the jet's acceleration in meters per second per second when taking off?
2
Do 100 J of work in 50 s and your power output is
2 W
A 2 kg mass has 40 J of potential energy with respect to the ground. Approximately how high is it above the ground?
2 m
A car has a mass of 1000 kg and accelerates at 2 meters per second per second. What is the magnitude of the net force exerted on the car?
2000 N
A car traveling at 22 m/s comes to an abrupt halt in 0.1 second when it hits a tree. What is the deceleration in meters per second per second of the car?
220
A karate chop delivers a blow of 3000 N to a board that breaks. The force that acts on the hand during this event is
3000 N
A bow is drawn so that it has 40 J of potential energy. When fired, the arrow will ideally have a kinetic energy that is
40 J
Using 1000 J of work, a toy elevator is raised from the ground floor to the second floor in 20 seconds. The power needed to do this job was
50 W
A skydiver, who weighs 500 N, reaches terminal velocity of 90 km/h. The air resistance on the diver is then
500 N
A diver who weighs 500 N steps off a diving board that is 10 m above the water. The diver hits the water with kinetic energy of
5000 J
A 10-N falling object encounters 4 N of air resistance. The net force on the object is
6 N
A 10.0 N force is pulling up on the ring of spring scale that weighs 2.0 N. If an 8.0 N mass is attached to the bottom hook of the scale, the scale reading would be
8.0 N
A 1-kg rock that weighs 9.8 N is thrown straight upward at 20 m/s. Neglecting air resistance, the net force that acts on it when it is half way to the top of its path is
9.8 N
Galileo
A force is required to change the motion of an object moving in a straight line. Heavier objects do not fall faster. DEMO: drop ball and crumpled sheet of paper Friction causes things to slow down and stop. DEMO: drop ball and paper in vacuum tube Ball rolling on inclined and horizontal planes DEMO: balls rolling down binder on carpet Natural tendency of an object is to resist a change in motion. This property is called inertia. In the absence of any force, something moving keeps moving in a straight line. DEMO: balls rolling down binder on tile No force is needed to keep the Earth moving forward - full credence is given to Copernican motion. DEMO: ball whirled on a string
FORCE CAUSES ACCELERATION
Acceleration is how fast velocity changes Acceleration is caused by a net force on an object Acceleration is directly proportional to the net force Acceleration α net force Double the force, double the acceleration; triple the force, triple the acc. DEMO: 1 student pushing a student in a chair vs. 2 students pushing the
ACCELERATION
Acceleration is how quickly velocity changes (how quickly speed and/or direction changes!) Acceleration = change of velocity/time interval It is the time rate of change of velocity, not the total change in velocity. Acceleration is a vector quantity. What three controls in am auto can cause acceleration? Accelerator (gas pedal), brake, steering wheel DEMO: ball on a string Twirled; Is it accelerating? Released: Is it accelerating? Porsche Taycan Turbo S 0-60 mi/hr in 3 s (actually 2.6 but let's not quibble) What is its speed at the end of 3 s? 60 mi/hr What is its velocity at the end of 3 s? Not enough information Pick forward direction on the track as positive: +60 mi/hr or 60 mi/hr in forward direction What is its acceleration? +20 mi/hr·s or 20 mi/hr·s forward 60-0 mi/hr in 3 s (I just made this number up) What is its speed at the end of 3 s? 0 mi/hr What is its velocity at the end of 3 s? 0 mi/hr What is its acceleration? -20 mi/hr·s or 20 mi/hr·s backward Turn the car around and go 0-60 mi/hr in 4 s What is its acceleration? -20 mi/hr·s or 20 mi/hr·s backward We already picked the first direction as forward, or positive Acceleration due to gravity, g = 9.8 m/s2 ≈ 10 m/s2 downward DEMO: drop ball When is acc = 0? When is vel = 0? DEMO: throw ball up in the air When is acc = 0? When is vel = 0? Free fall: ball dropped off a cliff Velocity after starting from rest with constant acceleration Velocity = acceleration × time v = at What is velocity at 1 s, 2 s, 3 s, 4 s, 5 s, 6 s, 7 s? Ball thrown in the air at 30 m/s Velocity after starting with some initial velocity with constant acceleration v = v0 + at What is velocity at 1 s, 2 s, 3 s, 4 s, 5 s, 6 s, 7 s (careful!)? How far something falls Distance traveled from rest with constant acceleration Distance = ½ acceleration × time × time = ½ at2 Derive this from d = average velocity × time Dropped ball What is distance at 1 s, 2 s, 3 s, 4 s, 5 s?
Natural tendency of an object is to be at rest
An object in its proper place will not move unless acted on by a force. Since Earth is in its proper place and a force to move it is inconceivable, the Earth is at rest.
Equilibrium of moving things
An object moving at constant speed in a straight line is in equilibrium. Its motion is not changing, so the net force is zero. Friction force: Pushing an object across the floor If we push it across the floor at constant speed, what is the balancing force to make the net force zero? Friction. If we push on the object and it doesn't move, what is the balancing force? Friction.
Natural Motion
An object will strive to get to its proper place determined by its "nature" or essence (earth, water, air, fire). Clay naturally falls to earth, smoke naturally rises in air Heavier objects fall faster (proportional to how much essence they have) Object rests when it is in its proper place
FORCES AND INTERACTIONS
Change our thinking about forces: instead of thinking of a force as a push or pull on another object, think of a force as an interaction between objects. You can't touch without being touched. Push on your neighbor's hand Push your fingers together Push your fingers on your desk When there is an interaction between two things, the interaction requires a pair of forces of equal magnitude and opposite direction. Push balloon against table Earth and Moon Rubber band between two fingers NY-LA analogy
Isaac Newton
Developed his famous laws of motion at age 23.
DEFINING YOUR SYSTEM
Don't action and reaction forces cancel each other out to produce a net force of zero? No, because the action and reaction forces are on different objects, or systems. Orange and apple example Orange system Orange and apple system Orange and apple system on the floor Pushing a dead car example: car is the system Inside pushing on the dashboard Outside pushing, on road or ice
FRICTION
Draw forces on a block on a table. What is ΣF? a? (i.e. PRACTICE BOOK, p. 23) At rest Pulled, but not moving Pulled at constant velocity Pulled, with acceleration DEMO: pull a block with a spring scale in each case above Friction acts any time two surfaces slide or tend to slide over one another. Caused by irregularities (can be microscopic) on the surface Direction of friction force is always in the direction opposing motion Static friction is a little larger than sliding friction This is why jamming your brakes and locking the tires (so that the tires slide) gives worse braking performance than a steady rolling stop (such that the tires always have static friction with the road). The force of friction Depends on the kinds of material in contact and how much they are pressing together (e.g. weight). For solids, does not depend on speed or area of contact. For fluids (water, air), speed and area are important: a big, fast airplane/boat pushes aside more air/water than small, slow ones. DEMO: show with spring scale
ACTION AND REACTION ON DIFFERENT MASSES
Earth and dropped ball Rifle and bullet
Copernicus
Earth circling the sun is the simplest way to account for observations of the motion of sun, moon, and planets. Doubted this idea because it did not make sense according to the accepted laws of motion.
acceleration
Fnet/m
FALLING OBJECTS
Free fall: When gravity is the only force acting on an object (no friction or air resistance), the object is in free fall. a = F/m, or g = W/m a = acceleration, F = force, g = acc. due to gravity, W = weight Double the mass of a falling object and you also double its weight g = W/m → g = 2W/2m = W/m Twice the gravitational force that produces acceleration is exerted on twice the inertia (mass) that resists acceleration. Acceleration due to gravity is independent of mass. DEMO: dropping steel ball and ping pong ball from standing, then from ladder Non-free fall: If air resistance acts on a falling object, then it is in non-free fall. Must keep in mind the idea of net force Draw the forces on an object falling in air. a = Fnet/m = (mg-R)/m, where R is air resistance R increases with the frontal area and speed of an object. DEMO: dropped paper Sheet vs. a ball Crumpled sheet vs. a ball Sheet beneath book CHECK QUESTION: Sheet on top of book When does a falling object stop accelerating? When weight = air resistance, i.e. when the object is falling fast enough that the air resistance is as large as the weight. This is called reaching terminal velocity. PRACTICE BOOK: page 24.
SPEED
How fast something moves Speed = distance/time Units: miles/hr, km/hr, m/s, etc. Instantaneous speed vs. Average speed Instantaneous speed: speed at a given instant Average speed = total distance covered/total travel time Batesville-Memphis speed? Usain Bolt won the 100 m with a time of 9.58 s. What is his average speed for the race? ~10.4 m/s What is his instantaneous speed at the beginning of the race? 0 m/s Is his top instantaneous speed in the race higher, lower or the same as 10.4 m/s? Higher
NET FORCE
If more than one force is acting on an object, then we consider the combination of forces, known as the net force. How are multiple forces combined? A force has magnitude and direction; any quantity that has magnitude and direction is called a vector . A vector sum takes the magnitude and direction of the forces into account when the forces are added together. Vector sum: ΣF DRAW: Fig 2.6 (applied and net forces on a block
MASS AND WEIGHT
Mass: the quantity of matter in an object Measured in kilograms (kg) The more mass, the more inertia or resistance to a change in motion DEMO: competition to shake big mass and little mass A fundamental quantity - it doesn't change from place to place Weight: the force upon an object due to gravity Measure in Newtons (N), the unit of force Define Newton, convert to pounds Weight is directly proportional to mass A non-fundamental quantity - it does change from place to place Weight on the moon is 1/6 the weight on the Earth; weight in deep space is zero. DEMO: lift objects to estimate weight DEMO: massive block hanging by a string
Violent Motion
Motion caused by pushing or pulling on an object (forces) Pushing a cart, lifting a weight, wind in a sail, bow & arrow DEMO: push book across table
NEWTON'S 2ND LAW OF MOTION
Newton's 2nd Law: the acceleration of an object is directly proportional 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. Acceleration α net force/mass a = Fnet/m What about acceleration = change in velocity/time interval? Acceleration is always in the direction of the net force
MASS RESISTS ACCELERATION
The property of mass to resist changes in motion, or acceleration, is inertia More mass, more inertia, less acceleration DEMO: 1 student pushing a light student in a chair vs. 1 student pushing more massive student Acceleration is inversely proportional to mass Acceleration α 1/mass Double the mass, half the acceleration; one third the mass, triple the acc. DEMO: sledgehammer steel block stacked on me while lying on a bed of nails DEMO: driving a nail on top of a student's head
VELOCITY
Velocity is speed plus direction, i.e. speed in a particular direction. DEMO: walking at the same speed in different directions Constant speed vs. constant velocity DEMO: release ball twirled on a string at different points in the path Batesville-Memphis/Memphis-Batesville velocities? Speed is a scalar quantity: magnitude (or amount) only Velocity is a vector quantity: magnitude and direction
SUPPORT FORCE
What forces act on a book lying at rest (in equilibrium) on a table? Weight, or force due to gravity Upward support force exerted by the table Equal in magnitude and opposite in direction to the weight because the net force must be zero. Compare to your hand compressing a spring; you exert a pushing force on the spring, and the compressed spring pushes back on your hand. The weight of the book pushes down on the atoms in the table, and the compressed atoms push back up on the book. The atoms' pushing is due to electric forces between atoms. Bathroom scale shows the support force necessary to balance your weight. What happens when you stand on two scales, one foot on each?
MOVING EARTH
When I jump in the air, why doesn't the wall slam into me? DEMO: ball dropped as I walk - where will it hit?
NEWTON'S 3RD LAW OF MOTION
Whenever one objects exerts a force on another object, the second object exerts an equal and opposite force on the first. To every action there is an equal and opposite reaction. Forces come in pairs: action and reaction, which together make an interaction. CHECK QUESTION: Identify action and reaction forces for: Hammering a nail Hitting a baseball Walking on the ground Dropped ball Rocket (DEMO: released balloon) DEMO: guys vs. girls tug-of-war What are all of the force pairs?
Non-free fall: If air resistance acts on a falling object, then it is in non-free fall.
a = Fnet/m = (mg-R)/m, where R is air resistance R increases with the frontal area and speed of an object.
acceleration
a= change in velocity/change in time a=v-vi/t
If an object of constant mass experiences a constant net force, it will have a constant
acceleration.
If the mass of an object does not change, a constant net force on the object produces constant
acceleration.
Which has zero acceleration? An object
all of these
Strictly speaking, more fuel is consumed by your car if an air conditioner, headlights, or even a radio is turned on. This statement is
almost always true.
A hydraulic press, like an inclined plane, is capable of increasing energy.
always false
An archer shoots an arrow. Consider the action force to be exerted by the bowstring against the arrow. The reaction to this force is the
arrow's push against the bowstring.
Suppose a particle is being accelerated through space by a 10-N force. Suddenly the particle encounters a second force of 10 N in the opposite direction from the first force. The particle with both forces acting on it
continues at the speed it had when it encountered the second force.
A skydiver jumps from a high-flying plane. As her velocity of fall increases, her acceleration
decreases
speed
distance/time
Newton's First Law of Motion
every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. DEMO: tablecloth and dishes Known as the Law of Inertia, it is a refinement of Galileo's concept of inertia. An object continues doing whatever it is doing unless a force acts on it. DEMO: coins, markers, hoop, bottle
A car that travels twice as fast as another when braking to a stop will skid
four time as far
freefall
g=10m/s^2
When a car is braked to a stop, its kinetic energy is transformed to
heat
EQUILIBRIUM RULE
if the net force on an object is zero, then it is in mechanical equilibrium (the net torque, or rotational component of force, must also be zero, but torque will wait until Chapter 8). Equilibrium Rule: ΣF = 0 DEMO: weight on a spring FIG: 2.14 DRAW: Practice Box, p. 31 Other ways of stating Newton's 1st Law: If the net force on an object is zero, then its velocity (speed and direction) doesn't change. If an object is in mechanical equilibrium, then its velocity doesn't change.
If an object's mass is decreasing while a constant force is applied to the object, the acceleration
increases.
Wherever the is an action force, there must be a reaction force which
is exactly equal in magnitude.
The force exerted by the road on each tire of an accelerating car
is less than the combined force of all four tires on the road.
weight
m x g
An object that has kinetic energy must be
moving
A horse exerts 500 N of force on a heavy wagon. The wagon pulls back on the horse with an equal force. The wagon still accelerates because
nevertheless there is still an unbalanced force on the wagon.
If you push for a half hour or a whole hour against a stationary wall,
no work is done in either case.
A woman carries a heavy box across a room at a constant speed. How much work does she do on the box while walking ?
none
A job is done slowly, while an identical job is done quickly. Both jobs require the same amount of work, but different amounts of
power
As a ball falls, the action force is the pull of the Earth's mass on the ball. The reaction force is the
pull of the ball's mass on the Earth.
A ball rolling down an incline has its maximum kinetic energy at
the bottom
A rocket becomes progressively easier to accelerate as it travels upward from the ground mainly because
the mass of the rocket decreases as fuel is burned.
Both A 50-kg sack is lifted 2 meters from the ground and a 25-kg sack is lifted 4 meters in the same time. The power expended in raising the 50-kg sack is
the same
average speed
total distance/total time
An object is propelled along a straight-line path by a force. If the net force were doubled, the object's acceleration would be
twice as much.
If an object is raised twice as high, its potential energy will be
twice as much.
If you find that twice as much work is needed to perform a task but it takes twice as much time, the amount of power required is
unchanged
When a falling object has reached its terminal velocity, its acceleration is
zero
Equilibrium rule
ΣF = 0