Cecily Zamora
Newton's three laws of motion describe the relationship between the motion of an object and the forces acting on it. Newton's third law relates to the conservation of momentum and can be applied to a variety of action-reaction force pairs in nature and everyday life. For example, when a fish swims, its fins push the water backward, and the water responds by pushing the fins and the fish forward. However, Newton's third law does not account for time delays between force changes and responses, which, according to the theory of relativity, must be at least as long as the time it takes light to travel between the objects.
| Characteristics | Values |
|---|---|
| When to apply Newton's Third Law | When the force exerted on an object changes |
| When not to apply Newton's Third Law | When the force exerted on an object changes suddenly |
| This is because there must be a time delay before the force that the second object exerts on the first can respond | |
| An object cannot | Exert a force on itself |
| All forces in the universe have | Corresponding reactions |
| Exceptions: fictitious forces in non-inertial reference frames | |
| Newton's Third Law relates to | The conservation of momentum |
| This remains true even when Newton's statement does not | |
| For example, when force fields and material bodies carry momentum | |
| Newton's Third Law can be observed in | Everyday life |
| For example, the swimming of a fish |
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What You'll Learn
Swimming of a fish
Newton's laws of motion explain the relationship between a physical object and the forces acting upon it. Newton's first law states that an object at rest will remain at rest unless acted on by an unbalanced force. This can be seen when a swimmer pushes off a wall or the bottom of a pool. The drag felt when movement starts is the static force that the swimmer is trying to overcome. Once a body is in motion, it wants to continue to stay in motion, which is why swimming becomes fluid after the initial movement.
Newton's second law talks about changes in momentum. It can explain why some people swim faster than others. For example, if two swimmers of the same weight push off a wall and don't take any strokes, the one who used the most force pushing off the wall will travel the furthest. This is because acceleration is greater for the person who produced the greater force, as both swimmers had the same mass.
Newton's third law of motion states that "action and reaction are equal and opposite". When a fish swims, using its fins to push water backward, it reacts by being propelled in the opposite direction, which is forward. The third law indicates that forces are always in pairs. As the fish swims, a net force between the oppositely directed forces does not cancel out.
However, it is important to note that Newton's third law is not always correct. If the force that an object exerts on another object suddenly changes, there must be a time delay before the force that the second object exerts can respond. This delay is at least as long as it takes a light ray to pass between the two objects. Therefore, as long as we restrict our investigations to time scales that are long compared to the time required for light to traverse the system, Newton's third law can be considered approximately correct. Additionally, according to Einstein's theory of relativity, information cannot travel faster than the speed of light, which contradicts Newton's third law.
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Jumping off a boat
Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that if object A exerts a force on object B, object B will exert an equal force on object A in the opposite direction. This law applies to all interactions between objects, regardless of their size, shape, or composition.
Now, let's consider the scenario of jumping off a boat and how Newton's third law applies in this situation:
When an individual jumps off a boat, they exert an upward force on themselves, propelling their body into the air. Simultaneously, according to Newton's third law, an equal and opposite force is exerted downward on the boat. This force causes the boat to accelerate in the opposite direction of the individual's jump. The magnitude of the acceleration of the boat depends on its mass and the force exerted during the jump.
The relative acceleration between the individual and the boat is crucial in understanding the application of Newton's third law in this scenario. If the boat has a significant mass compared to the individual, the acceleration of the boat will be smaller than that of the person jumping. On the other hand, if the boat is relatively lightweight, the acceleration of the boat may be more noticeable.
It's important to note that the force applied during the jump acts instantaneously, and the subsequent acceleration occurs immediately after. The forces and accelerations involved in jumping off a pier or a boat are relative to the masses and velocities of the objects involved.
In conclusion, when jumping off a boat, Newton's third law dictates that there is an equal and opposite reaction to the force exerted by the jumper. The boat accelerates in the opposite direction, and the magnitude of this acceleration depends on the mass of the boat and the force applied. Understanding the relative accelerations between the jumper and the boat provides insight into the application of Newton's third law in this specific context.
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Conservation of momentum
Newton's Third Law of Motion and the conservation of momentum are two fundamental laws of physics that govern the movement of objects in the universe.
Newton's Third Law
Newton's Third Law states that for every action, there is an equal and opposite reaction. In simpler terms, if an object exerts a force on another object, the second object will exert an equal force in the opposite direction. For example, when you push against a wall, the wall pushes back with the same amount of force. This principle also applies to objects in motion, such as a rocket propelling itself by expelling ignited propellant out of its engines, resulting in the rocket moving in the opposite direction.
Momentum is a property of moving objects and is calculated by multiplying the mass of an object by its velocity (mv). The conservation of momentum states that the total momentum of a system remains constant, assuming no external forces act on it. In other words, the total momentum of a system at one time must equal the total momentum at a later time. For instance, when a person on a skateboard throws a ball, the ball gains momentum (mbvb, where mb is the ball's mass and vb is its velocity). To maintain the total momentum of the system (skateboarder plus ball), the skateboarder must move in the opposite direction with equal momentum (my*vy). When the ball is caught by another person, the momentum is transferred, causing them to roll backward.
The conservation of momentum is closely related to Newton's Third Law. When an ice skater pushes off from a stationary position, the ice exerts an equal and opposite force, propelling the skater forward. Similarly, when a cannon is fired, the cannonball's momentum is matched by the recoil of the cannon in the opposite direction. These examples illustrate the principle of keeping everything in balance, where the momentum of one object or system is counterbalanced by the momentum of another.
While Newton's Third Law provides insights into the relationship between forces and motion, it does have limitations. For example, it does not account for time delays between forces acting on objects, as information cannot travel faster than the speed of light, as described by Einstein's theory of relativity. Nonetheless, by combining Newton's Third Law with the conservation of momentum, we can better understand the dynamics of objects and their interactions in the universe.
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Relativity and the velocity of light
Newton's third law states that if the force exerted on an object suddenly changes, there must be an immediate change in the force that the object exerts in response. However, this is only approximately correct when considering motions on time scales much longer than the time required for light to traverse the system. This is because, according to Einstein's theory of relativity, information cannot travel through the universe faster than the velocity of light in a vacuum.
Relativity is comprised of two related theories: special relativity and general relativity. Special relativity, proposed by Einstein in 1905, explains the relationship between space, time, mass, and energy. It states that the speed of light in a vacuum is the same for all observers, regardless of their location, motion, or the location and motion of the light source. This speed is denoted by a lowercase "c", which may stand for "constant" or the Latin "celeritas", meaning swiftness or celerity. As an object approaches the speed of light, its observed mass becomes infinitely large, and an infinite amount of energy would be required to propel it at the speed of light. Thus, it is impossible for any matter to travel faster than light speed.
Special relativity also describes several counterintuitive and experimentally verified phenomena, such as length contraction, Terrell rotation, and time dilation. Length contraction refers to the shortening of moving objects, while time dilation refers to the slowing of clocks in motion. Time dilation is described by the Lorentz factor, which quantifies the degree of time dilation and length contraction. As an object's speed approaches that of light, the Lorentz factor diverges to infinity, and an infinite amount of energy would be required to reach the speed of light.
General relativity, also proposed by Einstein, describes how gravity fits into the mix. Instead of viewing gravity as an invisible force pulling objects together, general relativity states that gravity is how mass warps space and time. Highly massive objects, such as stars, bend the path of light, and black holes, with their immense mass in a small volume, trap light due to the extreme warping of space. General relativity also explains the existence of muons, subatomic particles that are created when cosmic rays hit the Earth's atmosphere. Muons decay rapidly, in just 2.2 microseconds, and travel at nearly the speed of light. According to an observer on the Earth's surface, a muon should only travel 0.4 miles in its 2.2-microsecond lifetime, yet many muons reach the Earth's surface. This contradiction is resolved by understanding that time is measured differently in different frames of reference, an effect known as time dilation.
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An object cannot exert force on itself
Newton's laws of motion explain the relationship between a physical object and the forces acting upon it. Newton's first law states that an object at rest remains at rest, and an object in motion remains in motion at a constant speed and in a straight line unless compelled to change by an external force. This tendency to resist changes in the state of motion is called inertia. Newton's second law talks about changes in momentum (mass x velocity) per change in time.
Newton's third law of motion states that for every action, there is an equal and opposite reaction. In other words, when one body exerts a force on another body, the second body experiences a force that is equal in magnitude but opposite in direction to the force exerted. This means that in every interaction, there is a pair of forces acting on the objects. The magnitude of the forces is equal, but their direction is opposite. For example, a swimmer pushing against a pool wall with their feet will accelerate in the opposite direction to their push.
However, one corollary of Newton's third law is that an object cannot exert a force on itself. This is because, according to the law, there must be two interacting bodies for a force to be exerted. If an object were to exert a force on itself, it would violate the principle of equal and opposite reactions, as there would only be a single body involved.
Another corollary of Newton's third law is that all forces in the universe have corresponding reactions. The only exceptions are fictitious forces that arise in non-inertial reference frames, such as centrifugal and Coriolis forces in rotating reference frames.
While Newton's third law provides valuable insights, it is not always strictly accurate. For instance, if one object suddenly changes the force it exerts on another object, Newton's third law predicts an immediate change in the force exerted by the second object. However, this assumption contradicts Einstein's theory of relativity, which states that information cannot travel faster than the velocity of light in a vacuum. Therefore, there would be a time delay before the second object could respond, proportional to the distance between the objects.
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Frequently asked questions
Newton's third law can be applied when there is an interaction between two objects, even if the interaction is very short-lived.
Swimming of a fish is an example of Newton's third law. The fish's fins push the water backward, and the water reacts by pushing the fins forward, thus propelling the fish. Jumping off a boat is another example.
Yes, Newton's third law does not account for a time delay when the force exerted on an object suddenly changes. Einstein's theory of relativity states that information cannot travel faster than the velocity of light in a vacuum, contradicting Newton's third law. Additionally, an object cannot exert a force on itself, and fictitious forces that arise in non-inertial reference frames are exceptions.
