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Imagine a bus driving down the road when, suddenly, a bug flies into the windshield. In this case, the bug hits the bus, and the bus hits the bug.
Wrong! The fly and the bus experienced the same amount of force! Let us find out why. You are not the only one who initially thought that the bug experienced a greater force. Sir Isaac Newton's laws of motion have presented evidence to prove that both the bug and the bus experienced the same amount of force! These forces are the same in size but opposite in direction.
This is due to the fact that the bug's mass is way less than the bus. Therefore, the effect of the impact on the fly is more evident. The situation above describes how forces interact with each other. In this lesson, you will see many other examples of force interactions around us and will learn how Isaac Newton's advanced understanding of forces and motion is still relevant today! Force Interactions and Force Diagrams You may already know that the force of gravity pulls you to the center of the earth and keeps you from flying out into outer space. What you might find surprising is that you are also pulling on the earth.
To understand, you must first realize that force results from the interaction of two bodies. Newton discovered that whenever an object interacts with another object, they will exert force on each other. If the earth pulls you with a force of 300 N for example, you are also pulling the earth in the opposite direction with 300 N of force. This fundamental principle is Newton's third law of motion, or the law of action-reaction, which formally states: "For every action, there is an equal but opposite force of reaction." When you place a ball on a tabletop, the ball's weight is the action force that pushes the table downward. The table, on the other hand, will exert a reaction force on the ball that will push it upward. Let's identify and illustrate the pair of forces described above. In physics and engineering, the representation of forces acting on an object is shown in a free-body diagram or a force diagram. This is used to determine the effect of forces on the object's motion and resulting reactions. In a force diagram, forces are represented by arrows. The length of the arrows determines its strength while the arrowhead shows the direction in which the force is acting. These forces can be applied either horizontally along the x-axis or vertically along the y-axis. Look at these force diagrams for a box: The length of each arrow is the same, which means that each force acting on the box is the same amount. However, the arrows are pointing in opposite directions; which shows that the forces opposite as well. Diagram 1 has two forces along the horizontal, or the x-axis, that are the same strength but opposite in direction. Diagram 2 has two forces along the vertical, or y-axis, which are also the same strength and opposite in direction.
If you completed the first Related Lesson in this series, you will recall that the sum of all the forces, or the net force, acting on the box is zero if the forces are the same in strength but acting in opposite directions. This condition satisfies Newton's first law of motion that when an object's net force is zero, it will remain at rest or move at a constant speed in a specific direction. (If you have not completed the earlier Related Lessons yet, check them out in the right-hand sidebar!) Love a Pair!
Almost anything that you touch or have interaction with involves a force. A slight tap on the screen of your mobile device, for instance, involves action and reaction forces.
Explore the force pairs that exist within each of the following examples: Swimming In swimming, the arms of the swimmer will sweep the water to the back with a certain amount of force (action force). In return, the water pushes the swimmer forward (reaction force). The strength of the force of the hand bringing the water backward will be the same amount of force propelling or moving the swimmer forward. Watch Newton's 3rd Law - Why does a swimmer push the water backward?, from It's AumSum Time: An Inflated Balloon Similar to a real rocket ship, releasing the air from an inflated balloon demonstrates Newton's third law of motion. When the balloon is filled with air, the air pushes the inside walls of the balloon (action force). The inside walls of the balloon push the air back in the opposite direction (reaction force). Watch Balloon Rocket! Newton's Third Law of Motion., from Scientist Susan: Do the Math! Remember that when the object is at rest or moving at a constant velocity, the net force acting on it is zero. Newton's third law of motion supports this statement. Mathematically, we can express the net force acting on the object as the sum of the individual forces. Suppose we have the same ball on a tabletop where the ball exerts a force (F1) on the table, and the table exerts a force (F2) on the ball. We can find the net force (Fnet) with this equation: Fnet = (-F1) + F2 Note that we use -F1 for the force of the ball on the table because we choose a downward force to be negative. Suppose F1 is 10 N and F2 is also 10 N. You substitute these values into the equation: Fnet = (-10 N) + 10 N Fnet = 0 N A zero net force for the ball on the tabletop means that it is at rest. Time to review what you have learned with Wisc-Online's final video, Newton's Third Law of Motion: Now that you understand the basic principles and assumptions behind Newton's third law of motion, you are ready to explore more examples of its applications in the Got It? section!
Conservation of momentum: $$\sum p_{before}=\sum p_{after}\implies\\ p_{car,before}+p_{bug,before}=p_{car,after}+p_{bug,after}\implies\\ m_{car}v_{car,before}+m_{bug}v_{bug,before}=m_{car}v_{car,after}+m_{bug}v_{bug,after} $$ Assume the bug was still in the air before the hit, $v_{bug,before}=0$. After the hit, bug follows car $v_{car,after}=v_{bug,after}=v_{after}$. $$...\implies\\ m_{car}v_{car,before}=(m_{car}+m_{bug})v_{after}\implies\\ \frac{m_{car}}{m_{car}+m_{bug}}v_{car,before}=v_{after} $$ All this is just showing that since the bug's mass is so much smaller than the car's $m_{car}\gg m_{bug}$, the final velocity of the car is almost not changed at all, $v_{car,before} \approx v_{after}$. Momentum change: The bug accelerates to the car's speed in a very short time interval. This is an enormous momentum change seen from the bug, $$\Delta p_{bug}=p_{bug,after}-p_{bug,before}=p_{bug,after}=m_{bug}v_{after}$$ since $v_{bug,before}=0\ll v_{bug,after}$. The momentum change of the car is very small and almost none seen from the car's perspective, $$\Delta p_{car}=p_{car,after}-p_{car,before}=m_{car}v_{after}-m_{car}v_{before}\approx 0$$ since $v_{car,before} \approx v_{after}$. But this is only an approximation since the difference is negligible at this size-scale. In fact the momentum changes of the bug and car are exactly equal (but opposite): $$\sum p_{before}=\sum p_{after}\implies\\ p_{car,before}+p_{bug,before}=p_{car,after}+p_{bug,after}\implies\\ p_{car,after}-p_{car,before}=p_{bug,before}-p_{bug,after}\implies\\ \Delta p_{car}=-\Delta p_{bug} $$ So, yes, they do both experience the same momentum change! Newton's 2nd law of motion: $$\sum F=\frac{dp_{bug}}{dt}=\frac{\Delta p_{bug}}{\Delta t}$$ Since the collision time duration is very small while the momentum change of the bug is very big, the force is very very large on the bug. The poor bug's body simply cannot withstand that force and splats. Of course, the exact same force is exerted on the car from Newton's 3rd law. But as the car is much stronger and more massive this has extremely little effect. In the end it all comes down to the fragility and small mass of the bug - if it was a steel ball or a stone of the same size but much higher mass, the windshield migth be shattered. In much simpler and more intuitive words think of this: The bug is accelerated to the speed of the car; acceleration requires force, and so a large force seen from the bug's perspective is applied on the bug to cause this acceleration. That same force applied on a car of much, much larger mass gives almost no deceleration $F=ma$. |
Which force is larger when a bus collides with a bug and the bug splatters over the windshield?
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