Review. elenab/ Describing Motion: Kinematics in one dimension Kinematics is a part of mechanics, which is the description of.

Review

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Describing Motion:Kinematics in one dimension

Kinematics is a part of mechanics, which is the description of how objects move.

Speed

Speed is a measure of how fast object moves, measured by a unit of distance divided by a unit of time.

Instantaneous Speed

Average speed doesn’t indicate the different speeds that may have taken place during shorter time intervals.

Average Speed

average speed = total distance traveled/ time elapsed

Total distance traveled = average speed X time

1. What is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints 50 m in 2 s?

2. If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km.

(a) how far would it travel if it moved at this rate for 4 h?

(b) for 10 h?

3. In addition to speedometer on the dashboard of every car is an odometer, which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one half hour later, what has been your average speed?

4. Would it be possible to attain the average speed in previous example and never go faster than 80 km/h?

Velocity

When we describe speed and the direction of motion, we are specifying velocity

1. With what two physical values is the race-car driver concerned? Speed or velocity?

2. The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?

3. During certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed or a constant velocity?

1. How might you estimate your speed if the speedometer in your car is broken?

2. Which of the following can be used to measure an average speed: stopwatch, odometer, or speedometer? An instantaneous speed?

Acceleration

We can change the velocity of something by changing its speed; by changing its direction or by changing its speed and its direction.

Motion at Constant Acceleration

Acceleration is a rate of change , or change per second of velocity.

v= at

1. Which has the greater acceleration, an airplane that goes from 1000 km/h to 1005 km/h in 10 s, or a skateboard that goes from 0 to 5 km/h in 1 sec?

2. What is the acceleration of a race car that whizzes past you at a constant velocity 400 km/h?

Acceleration on Galileo Inclined Planes

Galileo found greater accelerations for steeper inclines. The ball attains max acceleration when the incline is tipped vertically.

-a ball rolling down an inclined plane is moving with constant acceleration

- greater accelerations for steeper planes, max acceleration when incline is tipped vertically

- regardless of weight and size, when air resistance is small enough to be neglected, all objects fall with the same unchanging acceleration.

We call this acceleration the acceleration due to gravity on the Earth, and we give it the symbol g.

g = 9.80 m/ s2 ~ 10 m/ s2

How Far?

With his inclined planes Galileo found that the distance a uniformly accelerating object travels is proportional to the square of the time

Distance = acceleration x time x time /2.

At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration

1. Which of the following (if any) could not be considered an “accelerator” in an automobile: gas pedal, brake pedal, steering wheel?

2. A sports car accelerates from 65 mph to 75 mph in 2 seconds while a minivan accelerates from 20 mph to 35 mph in 2 seconds. Which one has the larger acceleration?

3. You are standing on a high cliff above the ocean. You drop a pebble, and it strikes the water 4 seconds later. Ignoring the effects of air resistance, how fast was the pebble traveling just before striking the water? What is the height of the cliff?

Explaining Motion

Galileo’s inclined planes revisited

Slope downward – speed increases

Slope upward – speed decreases

No slope. Does speed change?

Initial Final position

Where is the final position?

Newton’s first law of motion

The first law incorporates Galileo’s idea of inertia and introduces a new concept, force.

Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change the state by forces impressed upon it.

Examples

1. Assume that you are pushing car across a level parking lot. When you are stop pushing, the car comes to stop. Does this violate Newton’s first law? Why?

2. Why does a tassel hanging from the rearview mirror appear to swing forward as you apply the brakes?

If you were traveling toward a distant star and you ran out of fuel, would your spaceship slow down and stop? Explain. 

Addition of Vectors – Graphical Methods

Examples

1. In everyday use, inertia means that something is hard to get moving. Is this the only meaning it has in physics? If not, what other meaning does it have?

2. How would you determine that two objects have the same inertia?

3. When a number of different forces act on an object, is the net force necessarily in the same direction as one of the individual forces? Why?

4. Modern cars are required to have headrests to protect your neck during collisions. For what type of collision are these headrests most effective?

Newton’s Second Law

The net force on an object is equal to its mass times its acceleration and points in the direction of acceleration

Fnet = ma

Examples

1. Forces of 4 N and 6 N act on the object. What is the minimum value for the sum of these two forces?

2. Two ropes are being used to pull a car out of a ditch. Each rope exerts a force of 700 N on the car. Is it possible for the sum of these two forces to have a magnitude of 1000N? Explain your reasoning.

3. If the net force on a boat is directed due east, what is the direction of the acceleration of the boat? Would your answer change if the boat had a velocity due north but the net force still acted to the east?

Examples

1. Describe the force(s) that allow you to walk across the room.

2. You are analyzing a problem in which two forces act on an object. A 200 N force pulls to the right, and a 40 N force pulls to the left. Your classmate asserts that the net force is 200 N because that is the dominant force that is acting. What is wrong with that assertion?

Net Force

The combination of forces that act on the object is the net force

Units of Force

1 newton (N) = 1 Kg *m/s2

1. You push on a crate that sits on a smooth floor and it accelerates. If you apply four times the pushing force, how much greater will be the acceleration?

2. Same for a rough surface.

Friction

If you apply a force to an object, a force of friction usually reduces the net force and resulting acceleration.

The direction of friction force is always in the direction opposing motion.

The force of dry friction between solid surfaces doesn’t depend on speed or area of contact.

Question

A jumbo jet cruises at constant velocity of 1000 km/h when the thrusting force of its engines is constant 100000 N.

1. What is the acceleration of the jet?

2. What is the force resistance on the jet?

Mass and Force of Gravity

Mass: The quantity of matter in an object. It is also the measure of the inertia or sluggishness, that an object exhibits in response to any effort made to start it, stop it, or change its state of motion in any way.

Force of Gravity= mg

Newton’s Second Law

The net force on an object is equal to its mass times its acceleration and points in the direction of acceleration

Fnet = ma

Important: acceleration of a body is always in the direction of net force!!!!

Free-body diagrams

Free fall revisited

When Acceleration is Less Than g – Nonfree Fall

Examples

1. Forces of 4 N and 6 N act on the object. What is the minimum value for the sum of these two forces?

2. Two ropes are being used to pull a car out of a ditch. Each rope exerts a force of 700 N on the car. Is it possible for the sum of these two forces to have a magnitude of 1000N? Explain your reasoning.

3. If the net force on a boat is directed due east, what is the direction of the acceleration of the boat? Would your answer change if the boat had a velocity due north but the net force still acted to the east?

Newton’s Third Law of Motion

Forces and Interactions

In a broader sense, a force is not a thing in itself but makes up an interaction between one thing and another.

Newton’s Third Law of Motion

Whenever one object exerts a force on a second object, the second exerts equal and opposite force on the first.

“On every action there is equal and opposite reaction”…

Which force we call action and which we call reaction doesn’t matter. The point is that neither exists without the other.

Action and Reaction on Different Masses

1. A car accelerates along a road. Identify the force that moves the car.

2. A high speed bus and an innocent bug have a head-on collision. The force of impact splatters the poor bug over the windshield. Is the corresponding force that bug exerts against the windshield greater, less or the same? Is the resulting acceleration of the bus greater than, less than or the same as that of the bug?

1. A skier is skiing down a steep slope, traveling at constant speed (that is, the skier has reached terminal velocity). What are the size and direction of the net force on the skier?

2. A car can accelerate at 2 meters per second per second when towing an identical car. What will its acceleration be if the towrope breaks?

3. If the number of different forces act on the object, is the net force necessarily in the same direction as one of the individual forces?

1. You apply a 75 N force to pull a child’s wagon across the floor at constant speed. If you increase your pull to 80 N, will the wagon speed up to some new constant speed, or will it continue to speed up indefinitely? Explain your reasoning.

2. You are riding an elevator from your tenth-floor apartment to the parking garage in the basement. As you approach the garage, the elevator begins to slow. What is the direction of the net force on you?

1. If the force exerted by a horse on a cart is equal and opposite to the force exerted by a cart on the horse, as required by Newton’s third law, how does the horse manage to move a cart?

2. A soft-drink sits at rest on a table. Which of the Newton’s laws explains why the upward force of the table acting on the can is equal and opposite to Earth’s gravitational force pulling down on the can?

3. A book sits at rest on a table. Which force does Newton’s third law tell us is equal and opposite to the gravitational force acting on the book?

Circular Motion

An object moving along a circular path at a constant speed must have a net force acting on it.

It is important to distinguish between adjectives centripetal (center-seeking) and centrifugal (center-fleeing).

The force, we are discussing , the centripetal force, is directed toward the center of the circle.

A Car, Rounding a Curve

Velocity and acceleration are perpendicular each other at each point of this circle.

Dynamics of Uniform Circular Motion

F = ma = m V2/R

Centripetal force is just a term, which means that there is the acceleration pointed to the center.

Projectile Motion

When something is thrown or launched

near the Earth surface,

it experiences a constant vertical gravitational force. Motion under these conditions is called projectile motion.

Important: The study of projectile motion is simplified because the motion can be treated as two mutually independent, perpendicular motions, one horizontal and the other vertical.

Question

Suppose a bullet is fired horizontally from a pistol and simultaneously another bullet is dropped from the same height.

Which bullet hits the ground first?

Important:The object projected horizontally will reach the ground in the same time as the object released vertically from the rest.

Fast Moving Projectiles: Satellites

The Earth satellite is simply a projectile that falls around the Earth rather than into it.

Question

A newspaper report reads in part, “ The space shuttle orbits Earth at an altitude of nearly 200 miles and is traveling at a speed of 18,000 mph. The shuttle remains in orbit because the gravitational force pulling it toward Earth is balanced by the centrifugal force (the force of inertia) that is pulling it away from Earth”. Explain why this newspaper should hire a new reporter.

Questions

1. What is the force that allows a person on roller-blades to turn a corner? What happens if this force is not strong enough?

2. A child rides on a carousel at constant speed. In which direction does each of the following vectors point?

a. velocity

b. change in velocity

c. acceleration

d. net force.

Questions

A vine is just strong to support Tarzan when he is hanging straight down. However, when he tries to swing from tree to tree, the same vine breaks at the bottom of the swing. How could it happen?