Seat belts and air bags save about a quarter of a million dollars a year.
Air bags combined with seat belts significantly reduce the risk of injury.
We didn't discuss the causes of the acceleration.
If you want to move by yourself, you need to either push off the floor or have someone pull you.
A magnet attracts or repels another magnet without touching it.
A sketch of a car.
In the sketch, we choose one object for detailed analysis.
The object that we choose to analyze is System A.
The system is the car.
The systems can have more than one object.
The wheels on the car can be part of a single system object.
We model an object like a car as a point-like object and ignore internal interactions in this chapter.
The motion of a system object can be affected by external interactions.
You could hold a bowling ball in one hand and a volleyball in the other.
Your hand pushes up hard to keep the bowling bal steady.
An arrow is used to represent the upward push on one of the balls.
The row is longer for the hand with the bowling bal than it is for the hand with the vol eybal.
The force that is exerted by the hand on the bal is represented by the arrow.
Representing external is a physical quantity that shows how hard an exter interaction is.
The symbol for force is the system.
The force's SI unit is called a newton.
The force that you exert when you hold a 100g bal is less than 1.0 N.
Earth puls downward on an object.
Since the bal is not moving, the two arrows for each bal should be the same length.
The air does push down.
Our hands are on the bowling ball.
Earth pulls down our confidence in the hypothesis when it happens.
The outcome and prediction can be on volleyball.
We are testing the hypothesis that the air exerts a downward force on objects.
Next, we put the ball and spring in a jar that is connected to a vacuum pump and will let the air out.
An experiment to determine the effect of air on a ball.
The air is moved to a spring.
The bal is supported by the upward force of the air on it.
This outcome is not normal.
You learn the mechanism by which air pushes up on objects when you study fluids.
We designed an experiment where we could predict the outcome using the hypothesis--the ball on a spring in a vacuum jar.
The spring should stretch less in a vacuum if the hypothesis is correct.
Something completely different happened after we performed the experiment.
The air's upward push on the ball is small.
The effect of air on objects can be ignored.
The system object was sent by a dot to show us how to model it.
The forces are represented by arrows.
A force diagram doesn't show us how a process changes with time, it shows the forces at a single instant.
This doesn't make a difference for processes in which no motion occurs.
We need to know if the force diagram changes as the object moves.
A small crater can be created by a rock dropping from above and sinking into the sand.
A force diagram is created after a rock touches the sand.
There is a dot at the side of the sketch.
The sand moves.
The force that the air exerts on the rock is assumed to be 6.
The downward-pointing arrow shows the force on the rock while the upward-pointing arrow shows the force on the sand.
The magnitudes of the forces are reflected in the lengths.
We will learn why they have different lengths later in the chapter.
We need to include arrows for external forces on the rock.
Since the sand is not part of the system, we don't use the rock's force on the sand in the force diagram.
The table is pushed up on the bottom and book A is on top of it.
Make a force diagram for book A.
We sketched the situation.
The system object is book A.
A force diagram is needed for book A.
Earth, the table, and book B are external environmental objects that exert force on book A.
C exerts no force on A.
Book B, table, and Earth are in the environment.
The book A is represented by a dot.
The force that the table exerts on book A and the force that book B exerts on book A are both on the same surface.
In this example, they were vertical forces, which does not mean normal.
You slide to the right on a wooden floor.
List the external objects that exert force on you and choose yourself as the system.
More than one object exerts a force on the system.
In this chapter, we limit our attention to the forces that point along one axis.
The process of lifting a suitcase.
A 50-N force pointed straight up is the same as the exerted along a vertical axis.
Remember that force is not static.
The sum can be found by adding two vectors to a system.
The sum vector is often called the resulting vector.
The sum of the force is not new.
For the system object to move.
The combined effect of the forces on the object is the sum of it.
The force diagram for system should not include the result of the net force forces that go from the tail of this.
The system and a spring are not stretched.
We put a golf bal into the bag to help the forces exert in each case.
Draw a diagram for each case.
The four situations are shown below.
The sum of the forces exerted on the system with a number of golf bal s is zero.
A trendline can be drawn.
The force that Earth exerts on the system balances the force that the spring exerts on it.
Force is a quantity with a direction and magnitude.
A method for determining the magnitude of a force is developed in the next conceptual exercise.
Force is a physical quantity that characterizes an action between two objects.
Just like a hug requires the interaction of two people, there must be two objects that interact.
Force doesn't reside in an object.
In this book, we must always identify the two interacting objects when speaking about force.
If you're thinking about a force that is exerted on a moving object and can't find another object that interacts with it, then you're thinking of something else.
A platform scale partially supports a book bag hanging from a spring scale.
The platform scale has 36 units of force and the spring scale has 28 units of force.
We drew the forces on the ball as being equal in magnitude when we drew a force diagram for it.
E on B continues to move in the same direction, but slows down.
The vertical forces add to zero and cancel each other in all the experiments.
The forces on the ball are only considered in the horizontal direction.
In the first experiment, the total of the forces on the ball is zero.
The sum of the forces are in the same direction as the velocity in experiment 2.
That is only one idea.
A gro cery cart moves in the direction the shopper pushes it, and a soccer bal moves in the direction the player kicks it.
Both ideas should be tested.
We compare the outcomes with the predictions.
We compare the two relationships to see if we can reject one of them.
S until she stops.
You throw a ball.
We can reject the predictions based on idea 1.
All outcomes are in line with the predictions based on idea 2.
We can now accept idea 2 with greater confidence, as a result of this idea and these testing experiments.
We looked at the simple things with motion diagrams and force diagrams.
The objects' motion and the sum of all forces that other objects exert on it were tested.
This analysis and testing yielded the above rule.
Make sure that the force diagrams and motion diagrams are consistent.
In the next conceptual exercise, we use information about the forces that external objects exert on a woman to answer a question about her motion.
We use known information about the motion to answer a question about an unknown force in the Try it Yourself question.
Before looking at the solutions, try to answer the questions yourself.
The force diagram is at constant speed.
She must point down.
The eleva idea is shown at the right.
She glides on rollerblades on a smooth surface.
The observer's refer ence frame is what determines our description of the motion of an object.
In this chapter, we assumed that all ob server were standing on Earth's surface.
In Section 2.3, we analyzed several experiments and concluded that if the forces exerted on one object by other objects add to zero, then the chosen object moves at 54 Chapter 2Newtonian Mechanics constant velocity.
Two people are watching a coffee mug.
He looks at a coffee mug that is sliding for it.
The mug's speed changes from zero to nonzero as seen by observer 1 even though there is no force on it.
Observer 2 is next to the car.
The mug is stationary with respect to her.
As the mug slides off the dashboard, the speed of the mug increases.
Observer 2 in Table 2.3 can account for what is happening using the rule relating the sum of the forces and changing velocity, but observer 1 cannot.
A passenger on a train might see her laptop computer start to move off her lap.
The rule we developed allows a person on the platform to explain the event.
The train started decreasing in speed as it approached the station, but the computer kept it constant.
The applicability of the rule depends on the reference frame of the observer.
A passenger in a car or train that is speeding up or slowing down is an observer in a noninertial reference frame.
Your body jerks forward when you are in a car that abruptly stops.
Even though nothing is pushing you in that direction, you are still into your seat.
You are an observer in a noninertial reference frame.
The law of univer inertial reference frames can be used to explain the changes in velocity of objects.
The ideas for his three laws of motion were put together by Observers in noninertial of light.
From now on, we will analyze phenomena mechanics from the point of view of observers.
Physicists analyzed the motion of thousands of objects from the point of view of observers in reference frames and found no discrepancies to the rule.
The first law of motion limits the reference frames with respect to which the other laws that you will learn in this chapter are valid.
Give an example.
When the sum of all forces ex erted on it is zero, an object does not change velocity and does not accelerate.
The sum of the forces that other objects exert on it is the same as the velocity change and accretion of the object.
If we know the forces on the object, we can predict the magnitude of its acceleration.
There are two forces that result in acceleration.
We use this information to create velocity-versus-time and track.
We repeat the same five experiments, only we make graphs for the cart when the forces of two different magnitudes pull it back on the cart in the negative direction.
We obtained the graph at the right using the five positive and five negative values of the force.
A man is pulling a bus.
The acceleration is zero when the sum of the forces is zero.
The object's resulting acceleration is constant if the sum of the forces exerted on it is constant.
The amount of matter must have an effect on the acceleration.
The force probe exerts the same force on the carts regardless of how many are being pul ed.
The pattern observed in Table 2.5 shows that the larger the amount of matter being pulled, the smaller the object's acceleration.
To measure the mass of an object, you need a standard unit of mass.
After the unit of mass has been chosen, the mass of all other objects can be determined.
The kilogram is a cylinder made of platinum-iridium that is stored in a museum.
Most countries have copies of this cylinder.
A quart of milk has a mass of about 1 kilo.
For example, if you exert a constant pul ing force on a 1.0- kilo object, and all other forces are balanced, you can measure its accelera tion.
You exert the same force on another object.
The measurement shows that it has half the force of the standard object.
Its mass is twice the standard mass.
This method isn't practical for everyday use.
We learn a method to measure the mass of an object that is easy to use in everyday life.
Our experiments show that when the same force is applied to two objects, the one with the greater mass has an accelerated speed.
The kilogram is a unit of mass.
Combining the two proportionalities into a single equation is possible.
We can use the unit of force to make an equation.
Physicists have given the force unit a special name because force is so ubiquitous.
A force of 1 newton causes an object with a mass of 1 kg to accelerate.
M>s2 is the weight of 1 N.
The Greek letter sigma means that you must add what you see.
The "vector sum of the forces" is not the sum of their magnitudes.
The magnitude of the vector sum is affected by directions.
Imagine an object with a lot of mass.
An infinitely massive object wouldn't change motion due to the finite forces on it.
Both extreme cases are understandable.
The acceleration on the left side is caused by the sum of the forces being exerted on the right side.
The reason for the accelera tion is not told in this operational definition.
To use it.
The forces being exerted on the system should be found.
The forces that point in the positive direction have a positive component, while the forces that point in the negative direction have a negative component.
After lifting for 0.50 s, we need to struct a force diagram for the suitcase.
The magnitude is reasonable and the unit for time is correct.
Since all the forces are equal to 0.50 m>s.
0.25 m is 0.50 m.
The lawn on M has the same magnitudes and point in different directions.
The mower's mass is 32 kilograms.
The horizontal acceleration of the mower is not caused by the force of magnitude you exert.
We can ignore them because of the grassy surface.
To sketch the situation, we chose the mower as the system and accelerated it.
The force diagram for the mower can be determined by substituting the known information into it.
The motion was sent by 32 kilograms.
We interact with the rounded answer to two significant digits because the known information had two significant digits.
The units are correct and the magnitude is reasonable.
Earth exerts a downward gravita.
We were given the mass of the lawn mower and the force that Earth exerts on it.
Imagine that we put a motion sensor at the top of the tube and drop objects of various shapes and sizes through it.
The motion sensor shows that all objects fall down with the same speed.
The mass of each object must be proportional to the Earth's gravity so that the mass cancels when we calculate the acceleration.
When calculating the force, it's better to use 9.8 N>kg instead of 9.8 m>s2.
The gravitational constant depends on the mass of Mars or the Moon.
We will not use the term "weight of an object" because it implies that weight is a second property of the object rather than an interaction between two objects.
The strategy will be applied to the sky dive of the diving champion.
He jumped from an airplane 3700 m above Lake Taupo in New Zealand.
His backup chute became tangled in its cords after his main parachute failed to open.
As he reached a 2-m high thicket of wild shrubbery, the partial y opened backup parachute slowed his descent to about 36 m/s.
The shrubbery decreased his speed before he reached the ground.
He had a collapsed lung and a broken ankle.
The man was stopped by shrubs and the ground at 36 m/s.
Estimate the force that was used to stop his fall.
We want to know how the process works.
Choose a coordinate system.
We useNewton's second law to find the average force that the shrubbery and ground exert on him while he is stopped, and his first law to find the average force that the shrubbery and ground exert on him while he is stopped.
We make appropriate simplify sume that the forces being exerted on him are con ing assumptions about the stant so that they lead to a constant acceleration.
A motion diagram for his motion while stop you neglect the size of the ping is shown along with the corresponding system object or neglect force diagram.
The force diagram is the same as the motion diagram.
The acceleration is constant.
The motion diagram shows the velocity change ar tent with each other and the diagrams must be longer to match it.
+324 m>s2 pressions and solve for the unknowns.
He is moving in the negative direction.
His initial position is +2.0 m at the top of the shrubbery, and his final position is zero at the ground.
His velocity in the negative direction is decreasing, which means the velocity change and the acceleration point in the opposite direction and whether the answer has been positive.
The shrubbery exerts an average magnitude of force.
The torial and graphical numbers are 22,680 kg # m>s2 + 686 N.
The results are consistent with the force diagram and motion diagram because the force is greater than Earth's.
The units are correct and the magnitude is huge.
The force exerted on Holmes by the shrubbery and ground is equal to the force that Earth exerts.
If he had stopped in a conservative 0.20 m with no help from the shrubbery, the ground would have exerted an average force on him.
Thanks to the shrubbery, the force was exerted over a large area of his body.
The shrubbery increased the stopping distance.
The force on him would have been greater if he had landed on dirt or something harder.
We used a roman type to indicate the unit of force.
Don't confuse these two looking notations.
The scale reading tells you how hard you are pushing on the scale.
The upward speed is increasing.
You have a mass of 50 kilograms.
The stationary elevator has a scale that reads 490 N.
The speed is constant.
The upward speed is decreasing.
The upward velocity is decreasing, so the acceleration points in the opposite direction.
In the middle of the trip, when the elevator moves at on, you change from one case to the next so that the sum.
The part of the trip that points downward is ond law.