Newton's Laws

Newton's Law of Inertia According to Newton's first law, an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force. It is the natural tendency of objects to keep on doing what they're doing. All objects resist changes in their state of motion. In the absence of an unbalanced force, an object in motion will maintain its state of motion. This is often called the law of inertia.

Now perhaps you will be convince of the need to wear your seat belt Now perhaps you will be convince of the need to wear your seat belt. Remember it's the law - the law of inertia. If the car were to abruptly stop and the seat belts were not being worn, then the passengers in motion would continue in motion. Assuming a negligible amount of friction between the passengers and the seats, the passengers would likely be propelled from the car and be hurled into the air. Once they leave the car, the passengers becomes projectiles and continue in projectile-like motion. The law of inertia is most commonly experienced when riding in cars and trucks. In fact, the tendency of moving objects to continue in motion is a common cause of a variety of transportation injuries - of both small and large magnitudes. Consider for instance the unfortunate collision of a car with a wall. Upon contact with the wall, an unbalanced force acts upon the car to abruptly decelerate it to rest. Any passengers in the car will also be decelerated to rest if they are strapped to the car by seat belts. Being strapped tightly to the car, the passengers share the same state of motion as the car. As the car accelerates, the passengers accelerate with it; as the car decelerates, the passengers decelerate with it; and as the car maintains a constant speed, the passengers maintain a constant speed as well. But what would happen if the passengers were not wearing the seat belt? What motion would the passengers undergo if they failed to use their seat belts and the car were brought to a sudden and abrupt halt by a collision with a wall? Were this scenario to occur, the passengers would no longer share the same state of motion as the car. The use of the seat belt assures that the forces necessary for accelerated and decelerated motion exist. Yet, if the seat belt is not used, the passengers are more likely to maintain its state of motion. The animation below depicts this scenario.

If the motorcycle were to abruptly stop, then the rider in motion would continue in motion. The rider would likely be propelled from the motorcycle and be hurled into the air. Once they leave the motorcycle, the rider becomes a projectile and continues in projectile-like motion. According to Newton's first law, an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force. It is the natural tendency of objects to keep on doing what they are doing. All objects resist changes in their state of motion. In the absence of an unbalanced force, an object in motion will maintain this state of motion. This is often called the law of inertia. The law of inertia is most commonly experienced when riding on the roadways. In fact, the tendency of moving objects to continue in motion is a common cause of a variety of transportation injuries - of both small and large magnitudes. Consider for instance the unfortunate collision of a motorcycle with a wall (or any obstacle in ints path). Upon contact with the wall, an unbalanced force acts upon the motorcycle to abruptly decelerate it to rest. The rider of the motorcycle would also be decelerated to rest if strapped to the motorcycle by seat belts or some form of safety harness (which is not necessarily a good idea - please read on!). Being strapped tightly to the motorcycle, the driver would always share the same state of motion as the motorcycle. As the motorcycle accelerates, the rider accelerates with it. As the motorcycle decelerates, the rider decelerates with it. And as the motorcycle maintains a constant speed, the driver maintains a constant speed as well. But what would happen if the rider were not wearing the seat belt? What motion would the rider undergo if she/he failed to use a seat belt and the motorcycle were brought to a sudden and abrupt halt by a collision with a wall or any other obstacle in its path? Were this scenario to occur, the driver would no longer share the same state of motion as the motorcycle. If a seat belt were used on a motorcycle, then the forces necessary for accelerated and decelerated motion would exist. Without a seat belt, the rider is more likely to maintain its state of motion. The animation below depicts this scenario.  

But why then are motorcycles not equipped with safety harnesses? But why then are motorcycles not equipped with safety harnesses? Is this a gross oversight made by motorcycle manufacturers? Absolutely not! While no transportation accident is safe, it is the goal of the manufacturers of all roadway vehicles to produce a vehicle which maximizes the safety of its riders. In the case of a motorcycle, it is believed that the rider's safety is maximized by not strapping the rider to the motorcycle. In a car accident, the safest place to be is in the car; yet in a motorcycle accident, the worst place to be is on the motorcycle. The reason? Cars are four-wheeled vehicles which have a stable platform capable of resisting sideways motion and resisting tipping over. As such, being strapped to the a car in an accident is an advantageous strategy for maximizing passenger safety. On the other hand, a motorcycle is a single-track vehicle (two wheels) which are prone to tipping over and sliding into and underneath the obstacles which they hit. Imagine being strapped to your motorcycle as you slide underneath a 2000-pound car. Being strapped to the motorcycle by a safety harness, you would share the fate of the motorcycle itself - being crushed by the 2000-pound car. Your chance of survival would be minimal. On the other hand, if you were to leave the motorcycle and be flung into the air, it is more likely that your hopeful impact with the ground would slowly alter your velocity as you skid to a stop over a lengthened period of time. Motorcycles are inherently dangerous vehicles; yet like all vehicles, manufacturers design them in a manner that maximizes rider safety. The omission of safety harnesses from motorcycles means that the motorcyclist does not share the same fate as the tipped over and skidding single-track vehicle.

If the truck were to abruptly stop and the straps were no longer functioning, then the ladder in motion would continue in motion. Assuming a negligible amount of friction between the truck and the ladder, the ladder would slide off the top of the truck and be hurled into the air. Once it leaves the roof of the truck, it becomes a projectile and continues in projectile-like motion. According to Newton's first law, an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force. It is the natural tendency of objects to keep on doing what they are doing. All objects resist changes in their state of motion. In the absence of an unbalanced force, an object in motion will maintain its state of motion. This is often called the law of inertia. The law of inertia is most commonly experienced when riding in cars and trucks. In fact, the tendency of moving objects to continue in motion is a common cause of a variety of transportation accidents - of both small and large magnitudes. Consider for instance a ladder strapped to the top of a painting truck. As the truck moves down the road, the ladder moves with it. Being strapped tightly to the truck, the ladder shares the same state of motion as the truck. As the truck accelerates, the ladder accelerates with it; as the truck decelerates, the ladder decelerates with it; and as the truck maintains a constant speed, the ladder maintains a constant speed as well.

Elephant and Feather - Free Fall Suppose that an elephant and a feather are dropped off a very tall building from the same height at the same time. Suppose also that air resistance could somehow be eliminated such that neither the elephant nor the feather would experience any air drag during the course of their fall. Which object - the elephant or the feather - will hit the ground first? Suppose that an elephant and a feather are dropped off a very tall building from the same height at the same time. Suppose also that air resistance could somehow be eliminated such that neither the elephant nor the feather would experience any air drag during the course of their fall. Which object - the elephant or the feather - will hit the ground first? The animation at the right accurately depicts this situation. The motion of the elephant and the feather in the absence of air resistance is shown. Further, the acceleration of each object is represented by a vector arrow. Many people are surprised by the fact that in the absence of air resistance, the elephant and the feather strike the ground at the same time. Why is this so? This question is the source of much confusion (as well as a variety of misconceptions). Test your understanding by making an effort to identify the following statements as being either true or false.

TRUE or FALSE: The elephant and the feather each have the same force of gravity. The elephant has more mass, yet both elephant and feather experience the same force of gravity. The elephant experiences a greater force of gravity, yet both the elephant and the feather have the same mass. On earth, all objects (whether an elephant or a feather) have the same force of gravity. The elephant weighs more than the feather, yet they each have the same mass. The elephant clearly has more mass than the feather, yet they each weigh the same. The elephant clearly has more mass than the feather, yet the amount of gravity (force) is the same for each. The elephant has the greatest acceleration, yet the amount of gravity is the same for each. If you answered TRUE to any of the above, then perhaps you have some level of confusion concerning either the concepts or the words force, weight, gravity, mass, and acceleration. In the absence of air resistance, both the elephant and the feather are in a state of free-fall. That is to say, the only force acting upon the two objects is the force of gravity. This force of gravity is what causes both the elephant and the feather to accelerate downwards. The force of gravity experienced by an object is dependent upon the mass of that object. Mass refers to the amount of matter in an object. Clearly, the elephant has more mass than the feather. Due to its greater mass, the elephant also experiences a greater force of gravity. That is, the Earth is pulling downwards upon the elephant with more force than it pulls downward upon the feather. Since weight is a measure of gravity's pull upon an object, it would also be appropriate to say that the elephant weighs more than the feather. For these reasons, all of the eight statements are false; there is an erroneous part to each statement due to the confusion of weight, mass, and force of gravity.

But if the elephant weighs more and experiences a greater downwards pull of gravity compared to the feather, why then does it hit the ground at the same time as the feather? Great question!! To answer this question, we must recall Newton's second law - the law of acceleration. Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. When figuring the acceleration of object, there are two factors to consider - force and mass. Applied to the elephant-feather scenario, we can say that the elephant experiences a much greater force (which tends to produce large accelerations. Yet, the mass of an object resists acceleration. Thus, the greater mass of the elephant (which tends to produce small accelerations) offsets the influence of the greater force. It is the force/mass ratio which determines the acceleration. Even though a baby elephant may experience 100 000 times the force of a feather, it has 100 000 times the mass. The force/mass ratio is the same for each. The greater mass of the elephant requires the greater force just to maintain the same acceleration as the feather. A simple rule to bear in mind is that all objects (regardless of their mass) experience the same acceleration when in a state of free fall. When the only force is gravity, the acceleration is the same value for all objects. On Earth, this acceleration value is 9.8 m/s/s. This is such an important value in physics that it is given a special name - the acceleration of gravity - and a special symbol - g.

A simple rule to bear in mind is that all objects (regardless of their mass) experience the same acceleration when in a state of free fall. When the only force is gravity, the acceleration is the same value for all objects. On Earth, this acceleration value is 9.8 m/s2. This is such an important value in physics that it is given a special name - the acceleration of gravity - and a special symbol - g.

But what about air resistance But what about air resistance? Isn't it nonrealistic to ignore the influence of air resistance upon the two object? In the presence of air resistance, the elephant is sure to fall faster. Right? 

why does the elephant fall faster? Suppose that an elephant and a feather are dropped off a very tall building from the same height at the same time. We will assume the realistic situation that both feather and elephant encounter air resistance. Which object - the elephant or the feather - will hit the ground first? The animation at the right accurately depicts this situation. The motion of the elephant and the feather in the presence of air resistance is shown. Further, the acceleration of each object is represented by a vector arrow. Most people are not surprised by the fact that the elephant strikes the ground before the feather. This question is the source of much confusion (as well as a variety of misconceptions).

TRUE or FALSE: The elephant encounters a smaller force of air resistance than the feather and therefore falls faster. The elephant has a greater acceleration of gravity than the feather and therefore falls faster. Both elephant and feather have the same force of gravity, yet the acceleration of gravity is greatest for the elephant. Both elephant and feather have the same force of gravity, yet the feather experiences a greater air resistance. Each object experiences the same amount of air resistance, yet the elephant experiences the greatest force of gravity

TRUE or FALSE: Each object experiences the same amount of air resistance, yet the feather experiences the greatest force of gravity. The feather weighs more than the elephant, and therefore will not accelerate as rapidly as the elephant. Both elephant and feather weigh the same amount, yet the greater mass of the feather leads to a smaller acceleration. The elephant experiences less air resistance and than the feather and thus reaches a larger terminal velocity. The feather experiences more air resistance than the elephant and thus reaches a smaller terminal velocity. The elephant and the feather encounter the same amount of air resistance, yet the elephant has a greater terminal velocity. If you answered TRUE to any of the above questions, then perhaps you have some confusion about either the concepts of weight, force of gravity, acceleration of gravity, air resistance and terminal velocity. The elephant and the feather are each being pulled downward due to the force of gravity. When initially dropped, this force of gravity is an unbalanced force. Thus, both elephant and feather begin to accelerate (i.e., gain speed). As the elephant and the feather begin to gain speed, they encounter the upward force of air resistance. Air resistance is the result of an objectplowing through a layer of air and colliding with air molecules. The more air molecules which an object collides with, the greater the air resistance force. Subsequently, the amount of air resistance is dependent upon the speed of the falling object and the surface area of the falling object. Based on surface area alone, it is safe to assume that (for the same speed) the elephant would encounter more air resistance than the feather.

All false The elephant and the feather are each being pulled downward due to the force of gravity. When initially dropped, this force of gravity is an unbalanced force. Thus, both elephant and feather begin to accelerate As the elephant and the feather begin to gain speed, they encounter the upward force of air resistance. Air resistance is the result of an object plowing through a layer of air and colliding with air molecules. The more air molecules which an object collides with, the greater the air resistance force. Subsequently, the amount of air resistance is dependent upon the speed of the falling object and the surface area of the falling object. Based on surface area alone, it is safe to assume that (for the same speed) the elephant would encounter more air resistance than the feather.

After all doesn't air resistance act to slow an object down But why then does the elephant, which encounters more air resistance than the feather, fall faster? After all doesn't air resistance act to slow an object down But why then does the elephant, which encounters more air resistance than the feather, fall faster? After all doesn't air resistance act to slow an object down? Wouldn't the object with greater air resistance fall slower?Answering these questions demands an understanding of Newton's first and second law and the concept of terminal velocity. According to Newton's laws, an object will accelerate if the forces acting upon it are unbalanced; and further, the amount of acceleration is directly proportional to the amount of net force (unbalanced force) acting upon it. Falling objects initially accelerate (gain speed) because there is no force big enough to balance the downward force of gravity. Yet as an object gains speed, it encounters an increasing amount of upward air resistance force. In fact, objects will continue to accelerate (gain speed) until the air resistance force increases to a large enough value to balance the downward force of gravity. Since the elephant has more mass, it weighs more and experiences a greater downward force of gravity. The elephant will have to accelerate (gain speed) for a longer period of time before there is sufficient upward air resistance to balance the large downward force of gravity.

Observe from the above diagrams and the above animation that the feather quickly reaches a balance of forces and thus a zero acceleration (i.e., terminal velocity). On the other hand, the elephant never does reach a terminal velocity during its fall; the forces never do become completely balanced and so there is still an acceleration. If given enough time, perhaps the elephant would finally accelerate to high enough speeds to encounter a large enough upward air resistance force in order to achieve a terminal velocity. If it did reach a terminal velocity, then that velocity would be extremely large - much larger than the terminal velocity of the feather.

So in conclusion, the elephant falls faster than the feather because it never reaches a terminal velocity; it continues to accelerate as it falls (accumulating more and more air resistance), approaching a terminal velocity yet never reaching it.

On the other hand, the feather quickly reaches a terminal velocity On the other hand, the feather quickly reaches a terminal velocity. Not requiring much air resistance before it ceases its acceleration, the feather obtains the state of terminal velocity in an early stage of its fall. The small terminal velocity of the feather means that the remainder of its fall will occur with a small terminal velocity.

Skydiving As the skydiver falls, he encounters the force of air resistance. The amount of air resistance is dependent upon two variables: The speed of the skydiver The cross-sectional area of the skydiver As the skydiver falls, he encounters the force of air resistance. The amount of air resistance is dependent upon two variables: The speed of the skydiver As a skydiver falls, he accelerates downwards, gaining speed with each second. The increase in speed is accompanied by an increase in air resistance (as observed in the animation below). This force of air resistance counters the force of gravity. As the skydiver falls faster and faster, the amount of air resistance increases more and more until it approaches the magnitude of the force of gravity. Once the force of air resistance is as large as the force of gravity, a balance of forces is attained and the skydiver no longer accelerates. The skydiver is said to have reached a terminal velocity.

The amount of air resistance is dependent upon two variables: The speed of the skydiver The cross-sectional area of the skydiver A skydiver in the spread eagle position encounters more air resistance than a skydiver who assumes the tuck position or who falls feet (or head) first. The greater cross-sectional area of a skydiver in the spread eagle position leads to a greater air resistance and a tendency to reach a slower terminal velocity. The importance of cross-sectional area to skydiving is also demonstrated by the use of a parachute. An open parachute increases the cross-sectional area of the falling skydiver and thus increases the amount of air resistance which he encounters (as observed in the animation below). Once the parachute is opened, the air resistance overwhelms the downward force of gravity. The net force and the acceleration on the falling skydiver is upward. An upward net force on a downward falling object would cause that object to slow down. The skydiver thus slows down. As the speed decreases, the amount of air resistance also decreases until once more the skydiver reaches a terminal velocity.