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<h1>Dynamics</h1>
<span class="subheading">Unit 2</span>
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<p><b>Dynamics</b> is known as the study of why things move and is the second branch of Mechanics. The foundation of Dynamics was laid out by famous astronoumer <b>Galileo Galilei</b> and later <b>Sir Issac Newton</b>. His work was widely spread throughout Europe and his book "Two New Sciences" opened the way to treating physics mathematically. For instance, he formulated that force was proportional to acceleration and laid the groundwork to what would become the creation of Newton's <b>Three Laws of Motion</b>. </p>
<img class="img-fluid" src="https://www.biography.com/.image/ar_1:1%2Cc_fill%2Ccs_srgb%2Cg_face%2Cq_auto:good%2Cw_300/MTY2MzU3Njc4ODI0NjI5OTM0/isaac_newton_1689_painting_sir_godfrey_kneller_public_domain_via_wikimedia_commons.jpg" alt="Sir Issac Newton" style="margin-left: 200px;">
<span class="caption text-muted">Sir Issac Newton</span>
<h1 id="in">Key Terms</h1>
<p>
<ul>
<li>Force: a push or pull that can change the orientation of an object; they are measured in Newtons(N) and are also vector quantities.</li>
<li>4 Fundamental Force:
<ol>
<li>(Fg)Gravitational Force: the attractive force that exists between all objects in the universe regardless if the object is in contact with anything else.</li>
<li>(EMF)Electromagnetic Force: force caused by electric charges over infinite distances(e.g. Electric Force & Magnetic Force)</li>
<li>Strong Nuclear Force: force that holds protons and neutrons together in the nucleus by overwhelming the electromagnetic force in a very short range.</li>
<li>Weak Nuclear Force: force responsible for creation and destruction of neutrons.</li>
</ol>
</li>
<li>Contact Forces:
<ul>
<li>(FN)Normal Force - force perpendicular to the surfaces of the objects that are in contact. The normal force is unique because it changes its magnitude depending on the force acting against it. <br></li>
For instance, a book on a table is being crushed by gravity but the normal force is resisting that force so that the book remains stationary.
<li>(Ff)Friction Force - force between objects in contact that is applied in the direction opposite to the attempted motion. The amount of friction force depends on the mass of the object, the quality of the surface, and the gravitational field strength.</li>
<li>(FT)Tension Force - force exerted by strings, ropes, fibres, chains, and anything like that.</li>
<li>(FA)Applied Force - force exerted by a human or an object on an object.</li>
</ul>
</li>
<li>Free Body Diagram(FBD): a diagram that shows all active forces on an object, that doesn't include the forces exerted on another object. The isolated object is drawn along with force vectors to represent the active forces.</li>
The size of the force vectors matter: a normal force is identically sized as the gravity force in a stationary object.<br>
<img class="img-fluid" src="img/post-sample-image - 副本 (9).jpg">
<span class="caption text-muted">FBD Examples</span>
<li>Net Force: the sum of all forces acted on an object for either horizontal or vertical forces; resultant force(vector)</li>
A stationary object would have a net force of zero, the gravity that is applied on it is "cancelled out" by the normal force.
<li>Mass: quantity of matter in an object. This property never changes unless matter is extracted from the object.</li>
<li>Weight: the measure of the force of gravity acting on an object. This property does change depending on the objects latitude and altitude, because the force of gravity is different in different places.</li>
<li>Inertia: the tendency of an object to remain at rest or in motion, which is measured by the object's mass.</li>
</ul>
</p><br>
<h1>Newton's Three Laws of Motion</h1>
<h2>Introduction</h2>
<p>
Newton's Three Laws of Motion reflect the behaviour of the motion of an object in certain situations.
<ol>
<li>Newton's first law of motion(Law of Inertia) were the continuation on the findings of famous astronoumer Galileo Galilei. The law states that objects will remain at rest or in a uniform motion in a straight line unless acted upon by an external unbalanced force. Basically it is the tendency of objects to remain unchanged.</li>
Let's say that I apply a force to a soccer ball on a completely frictionless(which is impossible) surface. The ball will continuously travel forward because friction or any other force isn't there to stop it. And a ball at rest will stay at rest.
<img class="img-fluid" src="https://cdn.mos.cms.futurecdn.net/pYtQzLeTQfLAZs8whBHa7k-1024-80.jpg.webp">
<span class="caption text-muted">Ball at Rest</span>
It is also why objects thrown in the air within the vehicle are unaffected by the movement because the object in the air has the tendency to continue moving.<br>
<li>Newton's second law of motion states that the acceleration of an object depends on the mass of the object and the amount of force applied to accelerate it(F=ma).</li>
<li>Newton's third law of motion states that "for every action, there is an equal and opposite reaction"(Fa=-Fa). This means that when you or an object applies a force(action force), that same magnitude of force will be exerted back onto that object(reaction force).</li>
A good example of this is throwing a tennis ball at a wall. The harder you throw the ball - or the more force you exert - the faster the ball will come back to you. This is because when the ball comes in contact with the wall, the ball exerts a force to the wall and the wall exerts that same magnitude of force back on to the ball. The reason the ball accelerates so much faster than the wall is due to the differences in mass. As seen in Newton's second law, acceleration is equal to the force divided by mass(a=F/m). The greater the mass, the lesser the acceleration. <br>
<img class="img-fluid" src="https://imagesvc.meredithcorp.io/v3/mm/image?url=https%3A%2F%2Fstatic.onecms.io%2Fwp-content%2Fuploads%2Fsites%2F12%2F2013%2F05%2Fwall-tennis-ball-400x400.jpg&w=1200&c=sc&poi=face&q=85">
<span class="caption text-muted">Tennis Ball Example</span>
</ol>
</p>
<h2>Air Resistance & Terminal Velocity</h2>
<p>
Air Resistance is the upward force exerted on an object as it falls. If there was no air resistance force, then skydivers would just fall towards the ground at unimaginable speeds.
When skydivers jump out, they first experience a stage of free fall which is when gravity is the only force acting on them. As the speed increases the air resistance will increase as well until eventually the two forces balance out and there is a constant velocity; this is the terminal velocity which is the maximum velocity reached upon when the forces of gravity and air resistance balance on a falling object.
<br><img class="img-fluid" src="img/post-sample-image - 副本 (11).jpg">
<span class="caption text-muted">Terminal Velocity Process</span>
</p>
<h2>Elevator</h2>
<p>
If we try to weigh ourselves(on a scale) in a moving elevator, the result may seem surprising. When you step on a scale, you are applying a weight(gravity) force to the scale and that scale is using that force to calculate your weight with appropriate units(kg, lbs, etc). So to solve for your weight in the elevator, we have to solve for the support force(or the normal force). <br>
When the elevator is at rest, your weight remains the same. When the elevator is moving at a constant velocity, your weight still remains the same because the elevator isn't acceleration and if a=0, then the net force(gravity and normal cancel) would also equal zero(F=m(0)=0). When the elevator is accelerating upwards, your weight will appear larger because the normal force is more upwards than your weight is downwards. When the elevator is accelerating downwards, the normal force with the floor is less upwards than your weight is downwards, so you appear lighter.
<img class="img-fluid" src="https://4.bp.blogspot.com/-W712Z8Ecm5k/VpneDwzQg4I/AAAAAAAABYc/OaMfFExS04o/s1600/elevator.png" style="margin-left:200px">
<span class="caption text-muted">Elevator Problem</span>
</p>
<h2>Coefficient of Friction</h2>
The Coefficient of Friction is ratio of the magnitude of the friction force(Ff) and the normal force(FN). It is the value that shows the friction relationship between objects and the normal reaction between them.
<br>(Max)Static Friction(Fs): the force required to accelerate an object forward which doesn't exist until an attempt is made to move it. It is the friction force that is active when an object is stationary.
<br>Kinetic Friction(Fk): the force that acts against a moving object's motion in the desired direction. It exists once the force applied in the desired direction is greater than the max static friction force. Typically the kinetic coefficient of friction is less than the coefficient of static friction. When the static friction force is equal to the applied force, the object is stationary thus has no acceleration. When the kinetic friction force is equal to the applied force, the object would be moving at a constant velocity thus has no acceleration as well.
<br>For instance, when you are pushing a heavy box on the floor. When the box is stationary, you need to apply a lot more force to accelerate it(static friction) and once accelerated, the box is easier to push(kinetic friction).
It can be visuallized with a graph that looks something like this:
<br><img class="img-fluid" src="img/post-sample-image - 副本 (10).jpg" alt="Graph of Force needed for Static & Kinetic">
<span class="caption text-muted">Static vs Kinetic Graph Comparison</span>
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