Chapter: Motion and Momentum Table of Contents Section 3: MomentumMomentum Section 1: What is...

Chapter: Motion and Momentum

Table of ContentsTable of Contents

Section 3: Momentum

Section 1: What is Motion?

Section 2: Acceleration

1818

• All matter in the universe is constantly in motion, from the revolution of Earth around the Sun to elections moving around the nucleus of an atom.

Matter and Motion11What is Motion?What is Motion?

• Something is in motion if it is changing position.

Changing Position

What is Motion?What is Motion?

• It could be a fast-moving airplane, a leaf swirling in the wind, or water tricking from a hose.

• When an object moves from one location to another, it is changing position.

11

• The runners sprint from the start line to the finish line.

Changing Position


• Their positions change, so they are in motion.

11

• An object changes position if it moves relative to a reference point.

Relative Motion


• Picture yourself competing in a 100-m dash.

• You begin just behind the start line.

• When you pass the finish line, you are 100 m from start line.

11

• If the start line is your reference point, then your position has changed by 100 m relative to the start line, and motion has occurred.

Relative Motion


11

• Displacement includes the distance between the starting and ending points and the direction in which you travel.

Distance and Displacement


• This figure shows the difference between distance and displacement.

11

• Speed is the distance traveled divided by the time taken to travel the distance.

Speed


• Speed can be calculated from this equation:

11

• In SI units, distance is measured in m and time is measured in s.

Speed


• As a result, the SI unit of speed is the m/s—the SI distance unit divided by the SI time unit.

11

• Average speed is found by dividing the total distance traveled by the time taken.

Average Speed


• An object in motion can change speeds many times as it speeds up or slows down.

11

• The speed of an object at one instant of time is the object's instantaneous speed.

Average Speed


• If it takes you 0.5 h to walk 2 km to the library, your average speed would be as follows:

11

• Average speed, instantaneous speed, and constant speed are illustrated here.

Average Speed


11

• You can represent the motion of an object with a distance-time graph.

Graphing Motion


• For this type of graph, time is plotted on the horizontal axis, and distance is plotted on the vertical axis.

11

Click box to view movie.

• Look at the graph.

Distance-Time Graphs and Speed


11

• According to the graph, after 1 s student A traveled 1 m.

• Student B, however, traveled only 0.5 m in the first second.

• So student A traveled faster than student B.



11

• The line representing the motion of student A is steeper than the line for student B.

• A steeper line on the distance-time graph represents a greater speed.



11

• A horizontal line on the distance-time graph means that no change in position occurs.

• If you are hiking in the woods, you want to know not only your speed, but also the direction in which you are moving.

Velocity


11

• The velocity of an object is the speed of the object and direction of its motion.

Velocity


11

• This is why a compass and a map are useful to hikers.

• Velocity has the same units as speed, but it also includes the direction of motion.

Velocity


11

• The velocity of an object can change if the object's speed changes, its direction of motion changes, or they both change.

Section CheckSection Check

11Question 1

To determine whether something has changed position, you need a _______.

A. compassB. global positioning systemC. mapD. reference point


11Answer

The answer is D. If someone starts a car and drives it 100 meters from its parking spot, the parking spot can be used as a point of reference to show that the car moved.


11Question 2

Displacement includes your _______ and _______ as well as the _______ in which you have traveled.


11Answer

It includes your starting point, ending point, and direction in which you have traveled. It is possible to have traveled a great distance and still have a displacement of zero if you traveled in an enormous circle and ended right where you began.


11Question 3

Speed equals distance divided by _______.

A. forceB. massC. timeD. velocity


11Answer

The answer is C. The smaller the t value in s=d/t, the greater the speed.

Acceleration and Motion

• Acceleration is the change in velocity divided by the time it takes for the change to occur.

• Acceleration has a direction.

• If an object speeds up, the acceleration is in the direction that the object is moving.

22AccelerationAcceleration

Acceleration and Motion

• If an object slows down, the acceleration is opposite to the direction that the object is moving.

• If the direction of the acceleration is at an angle to the direction of motion, the direction of motion will turn toward the direction of the acceleration.


Speeding Up • When an object that is already in motion

speeds up, it also is accelerating. • When the speed of an object increases, it is

accelerating.


• The toy car is accelerating to the right. Its speed is increasing.

Slowing Down • Acceleration occurs when an object slows

down, as well as when it speeds up. • The car is slowing down.


• During each time interval, the car travels a smaller distance, so its speed is decreasing.

Changing Direction

• Motion is not always along a straight line.

• If the acceleration is at an angle to the direction of motion, the object will turn.


• At the same time, it might speed up, slow down, or not change speed at all.

Changing Direction • Motion is not always along a straight line.

• If the acceleration is at an angle to the direction of motion, the object will turn.


• At the same time, it might speed up, slow down, or not change speed at all.

Click image to view movie.

Calculating Acceleration • If an object is moving in a straight line, its

acceleration can be calculated using this equation.


• In SI units, acceleration has units of meters per second squared (m/s2).

Positive and Negative Acceleration 22

AccelerationAcceleration

• So subtracting your initial speed from your final speed gives a positive number.

• As a result, your acceleration is positive when you are speeding up.

• When you speed up, your final speed always will be greater than your initial speed.

Positive and Negative Acceleration

• When your final speed is less than your initial speed, your acceleration is negative.


• Therefore, your acceleration is negative when you slow down.

Graphing Accelerated Motion

• The motion of an object that is accelerating can be shown with a graph.


• For this type of graph, speed is plotted on the vertical axis and time on the horizontal axis.

Graphing Accelerated Motion

• An object that is speeding up will have a line on a speed-time graph that slopes upward.


• An object that is slowing down will have a line on a speed-time graph that slopes downward.

• A horizontal line on the speed-time graph represents an acceleration of zero or constant speed.

22Section CheckSection Check

Question 1

A change in velocity divided by the time it takes for the change to occur equals the object’s _______.


22Answer

The answer is acceleration. Remember that, like velocity, acceleration has a direction. A car that takes a turn has changed its acceleration, even if nothing else changes.


Question 2

Imagine yourself driving a car down an empty stretch of road. How many ways could you change your acceleration?


22Answer

You could step on the gas; you could also step on the brake; you could turn the wheel, or do any combination of these.


Question 3

What is happening at point C in this speed-time graph?


A. the object is speeding upB. the object is slowing downC. the object is at restD. the object is gone


22Answer

The answer is B. When the line falls, the object is slowing down.

Mass and Inertia

• The mass of an object is the amount of matter in the object.

• In SI units, the unit for mass is the kilogram.

33MomentumMomentum

• The weight of an object is related to the object's mass.

Mass and Inertia

• Objects with more mass weigh more than objects with less mass.

• However, the size of an object is not the same as the mass of the object.

33MomentumMomentum

Mass and Inertia

• The more mass an object has, the harder it is to start it moving, slow it down, speed it up, or turn it.

• This tendency of an object to resist a change in its motion is called inertia.

33MomentumMomentum

• Objects with more mass have more inertia.

Momentum

• The momentum of an object is a measure of how hard it is to stop the object, and it depends on the object's mass and velocity.

• Momentum is usually symbolized by p.

33MomentumMomentum

Momentum

• Mass is measured in kilograms and velocity has units of meters per second, so momentum has units of kilograms multiplied by meters per second (kg . m/s).

• Momentum has a direction that is the same as the direction of the velocity.

33MomentumMomentum

Conservation of Momentum • According to the law of conservation of

momentum, the total momentum of objects that collide is the same before and after the collision.

• This is true for the collisions of billiard balls, as well as for collisions of atoms, cars, football players, or any other matter.

33MomentumMomentum

Using Momentum Conservation • There are many ways that collisions can

occur. • Sometimes, the objects that collide will

bounce off of each other.

33MomentumMomentum

• In other collisions, objects will stick to each other after the collisions.

• In both of these types of collisions, the law of conservation of momentum enables the speeds of the objects after the collisions to be calculated.

Sticking Together

• Imagine being on skates when someone throws a backpack to you.

• Before the student on skates and the backpack collide, she is not moving.

33MomentumMomentum

Sticking Together 33

MomentumMomentum

Sticking Together • Supposed a 2-kg backpack is tossed at a

speed of 5 m/s.

33MomentumMomentum

• Your mass is 48 kg, and initially you are at rest.

• Then the total initial momentum is

Sticking Together • After the collision, the total momentum

remains the same, and only one object is moving.

33MomentumMomentum

• You can use the equation for momentum to find the final velocity.

Colliding and Bouncing Off • Supposed two identical objects moving with

the same speed collide head on and bounce off.

33MomentumMomentum

• Before the collision, the momentum of each object is the same, but in opposite direction.

• So the total momentum before the collision is zero. Click image to view movie.

Colliding and Bouncing Off

• If momentum is conserved, the total momentum after the collision must be zero also.

33MomentumMomentum

• This means that the two objects must move in opposite directions with the same speed after the collision.


Question 1An object’s momentum can be increased either by increasing its _______ or its _______.


Answer

The answer is mass or velocity. A thrown baseball is harder to stop than a thrown ping-pong ball. At the same time, a baseball thrown by a professional pitcher is harder to stop than the same baseball lobbed by a fan.


Question 2Explain the law of conservation of momentum.

AnswerThis law says that the total momentum of objects in collision is always the same after the collision as it was before the collision.


Question 3Two objects of the same mass are moving directly toward each other at the same speed. What is the total momentum of the two objects?

AnswerThe total momentum is zero. This will be the same after the collision as well.

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