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**Newton’s Laws of Motion**

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**Newton’s 1st Law of Motion**

An object in motion tends to stay in motion and an object at rest tends to stay at rest, unless the object is acted upon by an unbalanced force. Also called the Law of Inertia

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**Newton’s 1st Law of Motion**

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**Inertia The resistance an object has to change its state of motion.**

The more MASS something has, the more inertia it has!

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We feel the effects of Newton's First Law every day, but usually don't notice them because other forces interfere. In space, the First Law is much more obvious. Objects will follow their natural path until they are stopped by an outside force. On Earth, the atmosphere will eventually slow down all moving objects, but in a vacuum (basically an empty space with no air or atmosphere), like space, it will be more obvious that objects obey Newton's Laws.

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**AnExample The person is standing on the floor.**

The only forces acting on the person are the force due to gravity pulling down & the normal force pushing up. The net force is zero and the person remains still.

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**Some everyday applications**

Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator. You amaze your friends by pulling a tablecloth out from under dishes on table To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted. Headrests are placed in cars to prevent whiplash injuries during rear-end collisions. While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object that abruptly halts the motion of the skateboard.

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How much force? A 2-kg object is moving horizontally with a speed of 4 m/s. How much net force is required to keep the object moving with the same speed and in the same direction? 0 N An object in motion will maintain its state of motion. The presence of an unbalanced force will change the velocity of an object.

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Is a force required? Yes, because even in outer space, an object has mass. If an object has mass then the object is going to resist changes in its motion. A force must be applied to set the object in motion. Newton’s Laws rule—Everywhere! If you were in a weightless environment in space, would it require a force to set an object in motion?

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**Newton’s Second Law of Motion**

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**Newtons’ Second Law Fnet = ma OR a = Fnet/m**

The acceleration of an object is directly proportional to the net force acting on the object… …and inversely proportional to the mass of the object.

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**NEWTON'S 2nd LAW OF MOTION**

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Graph of F vs. a If various known forces are applied to an object - one at a time and the corresponding accelerations are measured. The data are plotted. Since F and a are directly proportional, the relationship is linear. F a

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Slope of F vs. a Since slope = rise / run = F / a, the slope is equal to the mass. If y = m x + b, y corresponds to force, m to mass, x to acceleration, and b (the y-intercept) is zero. F a

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**a = 4 m/s2 Example F= ma a = F/m a = 120000 N/30000 kg**

How much acceleration does a 747 jumbo jet of mass 30,000kg experience in takeoff when the thrust of all of the engines is 120,000N? F= ma a = F/m a = N/30000 kg a = 4 m/s2

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**Example The same net force is applied to two blocks.**

If the blue one has a smaller mass than the yellow one, which one will have the LARGER acceleration?

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**More about mass Mass is an inherent property of an object**

Mass is independent of the object’s surroundings Mass is a scalar quantity The SI unit of mass is kg

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**Mass vs. Weight …Mass and weight are two different quantities**

Weight is equal to the magnitude of the gravitational force exerted on the object Weight will vary with location Weight is not an inherent property of the object Example: wearth = 20 N; wmoon ~ 3.3 N mearth = 2 kg; mmoon = 2 kg

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Gravitational Force The gravitational force, Fg is the force that the earth exerts on an object Another name for this force is weight! It is directed toward the center of the earth Fg (or weight) = ma where a is acceleration due to gravity

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**If the NET FORCE is parallel to the velocity, then the speed of the object increases.**

If the NET FORCE is anti-parallel (or opposite) to the velocity, then the speed of the object decreases.

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**If the net force is perpendicular to the velocity, the direction of the velocity changes.**

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**When Acceleration Is Zero...**

…the net force is zero. …we say the object is in Mechanical Equilibrium. For Static Equilibrium the velocity is zero. For Dynamic Equilibrium the velocity is constant.

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**Example - Static Equilibrium**

Calculate the mass of the picture. Weight down

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Example Goblin 400 N Ogre 1200 N Troll 850 N Treasure 300 kg A troll and a goblin are fighting with a big, mean ogre over a treasure chest, initially at rest. Find: Fnet a v after 5 s x after 5 s = 50 N left = m/s2 left = m/s left = m left

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Example A 3 kg watermelon is launched straight up by applying a 70 N force over 2 m. Find its max height. Phase I: the launch Draw pic and find net force. Calculate a during launch. Calculate vf at the end of the launch (after 2 m). 40.6 N up m/s2 m/s Phase II: freefall Draw pic and think about what a is now. vf from phase I is v0 for phase II. What is vf for phase II? Calculate max height & add 2 m. -9.8 m/s2 -9.8 m/s2 zero 4.76 m

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Example Consider an elevator moving downward and speeding up with an acceleration of 2 m/s2. The mass of the elevator is 100 kg. Ignore air resistance. What is the tension in the cable? Identify Forces: Tension in cable, weight of the elevator Draw freebody diagram Chose coordinate system: Let up be the +y direction and down –y. Then : Translate the FBD into an algebraic expression. T-W = m(-a) so T-(100 kg)(9.8 m/s2) = (100 kg)(-2 m/s2) v T W=Fg earthelevator. a

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Newton’s 3rd Law For every action there is an equal and opposite reaction. Book to earth Table to book

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Think about it . . . What happens if you are standing on a skateboard or a slippery floor and push against a wall? You slide in the opposite direction (away from the wall), because you pushed on the wall but the wall pushed back on you with equal and opposite force. Why does it hurt so much when you stub your toe? When your toe exerts a force on a rock, the rock exerts an equal force back on your toe. The harder you hit your toe against it, the more force the rock exerts back on your toe (and the more your toe hurts).

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Action - Reaction If you hit a tennis ball with a racquet, the force on the ball due to the racquet is the same as the force on the racquet due to the ball, except in the opposite direction. If you drop an apple, the Earth pulls on the apple just as hard as the apple pulls on the Earth. If you fire a rifle, the bullet pushes the rifle backwards just as hard as the rifle pushes the bullet forwards.

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**Force vs. difference in effects**

How could the forces on the tennis ball, apple, and bullet, be the same as on the racquet, Earth, and rifle? The 3rd Law says they must be, the effects are different because of the 2nd Law! 0.40 kg A 0.40 kg apple weighs 3.92 N (W = mg). The apple’s weight is Earth’s force on it. The apple pulls back just as hard. So, the same force acts on both bodies. Since their masses are different, so are their accelerations (2nd Law). The Earth’s mass is so big, it’s acceleration is negligible. apple 3.92 N Earth 3.92 N 5.98 1024 kg

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**a = m a m Apple’s Earth’s little mass big mass**

The products are the same, since the forces are the same. a = m m a Apple’s little mass Earth’s big mass Earth’s little acceleration Apple’s big acceleration

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Newton’s Third Law A bug with a mass of 5 grams flies into the windshield of a moving 1000kg bus. Which will have the most force? The bug on the bus The bus on the bug

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**Newton’s Third Law The force would be the same. Force (bug)= m x A**

Force (bus)= M x a Think I look bad? You should see the other guy!

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Normal Forces Many times the normal force is equal and opposite to the weight of an object If the following conditions are satisfied, then N = mg: The object is on a level surface. There’s nothing pushing it down or pulling it up. The object is not accelerating vertically.

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**Cases in which N mg a Mass on incline**

Applied force acting on the mass Nonzero acceleration, as in an elevator or launching space shuttle FA N N a N mg mg mg

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**N and mg are NOT an Action-Reaction Pair!**

“Switch the nouns to find the reaction partner.” Earth FE m mg N Fg The dot represents the man. mg, his weight, is the force on the man due to the Earth. FE is the force on the Earth due to the man. N, the normal force, is the force on the man due to the ground. Fg is the force on the ground due to the man. The red vectors are an action-reaction pair. So are the blue vectors. Action-reaction pairs always act on two different bodies!

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Misconceptions If an object is moving, there must be some force making it move. Wrong! It could be moving without accelerating. The force that set it in motion is in the past. If v = 0, then a and Fnet must be zero. Wrong! Think of a projectile shot straight up at its peak. An object must move in the direction of the net force. Wrong! It must accelerate that way but not necessarily move that way.

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**Misconceptions (cont.)**

Heavy objects must fall faster than light ones. Wrong! The rate is the same in a vacuum. When a big object collides with a little one, the big one hits the little one harder than the little one hits the big one. Wrong! The 3rd Law says they hit it each other with the same force. If an object accelerates, its speed must change. Wrong! It could be turning at constant speed.

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