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Motion Newton’s Laws LabRat Scientific © 2018 F = Ma
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Historical Reference Aristotle Galileo Galilei Newton 384 – 322 BC
Developed the Greek concept of “natural position” for objects Felt that the real world too complex, so experimentation was useless Galileo Galilei 1564 – 1642 Popularize the “experimental” approach Famous for his Falling Body experiments (among other things) Newton 1642 – 1727 Laws of Motion Law of Universal Gravitation Consolidated the concepts of Calculus
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This lesson will focus on the work of Isaac Newton…
Historical Reference This lesson will focus on the work of Isaac Newton… Newton 1642 – 1727 Laws of Motion Law of Universal Gravitation Consolidated the concepts of Calculus
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Newton’s First Law An object in motion tends to stay in motion and an object at rest tends to stay at rest until acted on by an unbalanced external force.
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Newton’s First Law An object in motion tends to stay in motion and an object at rest tends to stay at rest until acted on by an unbalanced external force. If we remove the opposing force, the object will begin to move…
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Newton’s First Law An important aspect to this first law is that it deals with a “change in motion” If an object is at rest, we can conclude it’s being acted on by balanced forces In general, an object is always subjected to some force or another. Gravity comes to mind… If an object is in “uniform constant motion” where the velocity is not changing, we can conclude that any forces acting on the object are also balanced Example: Friction being opposed by an equal and opposite thrust
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Let’s do a little thought experiment to drive this idea home…
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Newton’s First Law In the situation at the right, is it reasonable to assume the forces acting on the vase are balanced? Yes, it is reasonable to assume the table and vase are not moving (no change in velocity). This means the forces must be balanced.
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Newton’s First Law The downward gravity force (a.k.a. weight) is counteracted by an upward force being created by the table. We should also note that since the table is not moving downward, the floor must be pushing upward to counteract the weight of the table and the vase…
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Newton’s First Law What happens if we quickly pull the table out from under the vase? First, the forces acting on the vase become unbalanced... Then the vase reacts to the unbalanced forces and begins to move in the direction of the remaining force – downward.
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Let’s skip Newton’s 2nd Law for the time being and take a look at his 3rd Law…
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Newton’s Third Law For every action there is an equal and opposite reaction.
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Newton’s Third Law For every action there is an equal and opposite reaction. Sally pushes on Joe… Push
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(Newton’s First Law says so…)
They will both move forever unless a new external force causes them to move differently (Newton’s First Law says so…)
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Let’s do another little thought experiment to drive this idea home…
Can we take advantage of Newton’s 3rd law to get something to start moving?
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Newton’s Third Law implies that if Sally were to push on (throw) bowling balls, she could get herself to move…
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Newton’s Third Law Once Sally stops throwing bowling balls, she will keep moving to the left (assuming there are no other imbalanced lateral forces acting on her).
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Newton’s Third Law Once Sally stops throwing bowling balls, she will keep moving to the left (assuming there are no other imbalanced lateral forces acting on her).
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Newton’s Third Law Once Sally stops throwing bowling balls, she will keep moving to the left (assuming there are no other umbalanced lateral forces acting on her).
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Newton was smart enough to figure out what was needed to get things moving.
Was he smart enough to come up with a way to predict motion? Of course he was…
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Newton’s 2nd Law The Force acting on an object is directly proportional to the Mass of the object and the object’s Acceleration. F = M * a But this isn’t the most useful form of the equation…
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F a = ------ M Newton’s 2nd Law
The Acceleration of an object is directly proportional to the Force acting on the object and indirectly proportional to the Mass of the object. F a = M
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Newton’s 2nd Law So, if we can apply a force to an object (which has mass, of course) we can get it to accelerate… Let’s make the object a rocket. If the rocket accelerates, that means it will start moving... Not only will it start moving, it will go faster and faster as long as we continue to apply the force.
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Newton’s 2nd Law Before we look at how Newton’s Laws affect the motion of a rocket, let’s look at the simple problem of a free falling object… Force Accel = Mass Force = the Gravitational Force = Weight Weight Weight Mass = = Accel Due to Gravity ft/sec2
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Weight (lbs) Accel = lbs Mass 32.2 ft/sec2
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Accel = ----------------------------- ------------------- 32.2 ft/sec2
lbs Accel = 32.2 ft/sec2 ft/sec2 Accel = lbs x lbs Applying some algebra… This shows that the acceleration of the free falling object is independent of the object’s mass… Accel = ft/sec2
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From this simple mathematical exercise, we have theoretically proven that objects of different masses will fall with the same acceleration and instantaneous speed, and ultimately hit the ground at the same time (as long as we neglect air drag). This is contrary to the thinking of Aristotle who argued that objects had desired natural positions. The natural position of a solid object like a ball was on the ground – that’s why it falls downward. He also felt that the heavier the object, the greater its “desire” to get to its natural position. As such, the a heavier ball would hit the ground the light ball…
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Develop a simple experiment to see who is right…
VS.
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A rocket blasting off from a launch pad.
Let’s look at one more thought experiment to wrap up all these concepts… A rocket blasting off from a launch pad.
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When the rocket is sitting waiting to be launched……
The rocket applies a downward force on the launch pad… The launch pad in turn, is applying an upward force on the rocket… Since the motion of the rocket is not changing, the forces must be balanced…
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3… 2… 1…
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Ignition!
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After the rocket motor is ignited, the rocket motor begins producing a force…
The upward force of the thrust causes the downward force of the rocket to get smaller… As the rocket gets “lighter” the launcher doesn’t have to push upwards with as much force… However, the launcher must still push upwards until enough thrust is generated to over come the remaining downward force of the rocket.
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Once the thrust becomes great enough, it overcomes the weight of the rocket. At this point the forces are no longer balanced – in other words, a force “imbalance” exists… Newton says the rocket will now begin to move!
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Once the thrust becomes great enough, it overcomes the weight of the rocket. At this point the forces are no longer balanced – in other words, a force “imbalance” exists… Newton says the rocket will now begin to move!
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Once the thrust becomes great enough, it overcomes the weight of the rocket. At this point the forces are no longer balanced – in other words, a force “imbalance” exists… Newton says the rocket will now begin to move!
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Once the thrust becomes great enough, it overcomes the weight of the rocket. At this point the forces are no longer balanced – in other words, a force “imbalance” exists… Newton says the rocket will now begin to move!
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Let’s look at the math… Forces Thrust - Weight - Drag
Since the rocket isn’t moving very fast we can neglect drag. Forces Thrust Weight Drag a = = Mass Mass Forces Thrust Weight a = = Mass Mass Let’s put in some values and see what the results look like. Forces lbs lbs a = = Mass (100 lbs / ft/sec2) Forces lbs a = = Mass lbs / (ft/sec2)
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Let’s look at the math… Forces - 50 lbs
Mass lbs / (ft/sec2)
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Let’s look at the math… Forces - 50 lbs
Mass lbs / (ft/sec2) a = ft/sec2 The “negative” acceleration indicates it’s a downward acceleration - similar to the “- 1G” (-32.2.ft/sec2) that is pulling us towards the floor right now… While there is still a downward acceleration (which by default also means a downward force) the launch pad must still support part of the weight of the rocket. As the thrust builds, it will eventually overcome the rocket’s weight…
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Let’s look at the math… (T) (W)
Forces lbs lbs a = = Mass lbs / (ft/sec2) What does the acceleration look like when the thrust is greater than the weight? a = ft/sec2 The “positive” acceleration indicates it’s an upward acceleration The rocket will begin moving upward…
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Questions ?
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