Newton’s Laws Chapter 5 Physics 521

Introduction Our understanding of force and motion has progressed with time. Sir Isaac Newton published his laws in 1686 and we still use them today to predict force and motion interaction for macroscopic objects.

Force and motion are divided into 2 branches: Classical or Newtonian Mechanics which treats energy and matter as separate things and uses Newton’s laws to predict the results of objects interacting. ▫ It provided connections between acceleration and forces acting on objects. ▫ Deals with larger objects. Quantum Mechanics attempts to explain motion and energy of atoms and subatomic particles.

Newton’s 1 st Law – Law of Inertia An object with no net force acting upon it remains at rest (if it was at rest) or remains in motion (if it was in motion), and it moves with a constant velocity in a straight line. Objects tend to keep doing what they are already doing. Ex. If you leave a book on a desk, you expect it to be there when you return – no net force. ▫ A hockey puck on an air table will move in a straight line indefinitely because of its own inertia.

Recall … Inertia –an object’s resistance to a change in its motion. Net force – the sum of all forces acting on an object. It is the net force that causes an object to accelerate.

Definitions Equilibrium – the state when there is no net force acting on an object. Inertial frame of reference – object is at rest or has a constant velocity; Newton’s laws apply. ▫ Ex. You are inside a windowless, perfectly smooth riding tractor trailer, that is moving at a constant velocity. You have no way of knowing if you are moving or not. Whatever happens to you inside that trailer follow the laws of motion.

Non-inertial frame of reference – object is accelerating; Newton’s laws do not apply. ▫ Ex. You are traveling in a car that suddenly and quickly decelerates. You feel as if you are being thrown forwards, when in reality your body just wants to keep its inertia (forward motion) until a force (seatbelt) causes a change in the inertia. ▫ No force has caused you to move forward.

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Newton’s 2 nd Law The acceleration of an object is directly proportional to the net force on it and inversely proportional to its mass. The direction of the acceleration is the same as that of the net force. Therefore: or Example: if you push a desk there is a net force because your applied force is greater than the force of friction and the desk accelerates.

Newton’s 2 nd law states that the force that causes a mass (m) to accelerate (a) is the net force (F net ) acting on the mass. F net is the vector sum of all the forces involved whether it be the applied force (F A ) and frictional force (F f ) or the force of gravity (F g ) and the normal force (F N ).

You must be careful and watch the signs. Horizontal motion: Vertical motion: We will combine dynamics and kinematics equations to fully analyze motion.

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Dynamics Test 1

Newton’s 3 rd Law The Law of Action-Reaction When an object exerts a force on a second object, the second object exerts an equal force on the first but in the opposite direction. Ex. ▫ You hit a wall, it “hits” you just as hard ▫ You shoot a gun, the bullet goes forward and the gun ‘kicks back’. ▫ You jump forward from a rowboat onto a dock and the boat goes backward.

▫ A falling boulder is accelerated toward Earth, but Earth is also pulled upward by the boulder with an equal force. We don’t notice the Earth’s acceleration, because if you recall from Newton’s 2 nd law, acceleration is inversely proportional to mass. Since the Earth is so massive, its acceleration is very, very small.

Forces always act in pairs. Action-Reaction forces act on different objects so they do not cancel each other out and give a net force of zero. Ex. ▫ If you kick a football, the action force is on the ball, and it is basically the only force on the ball so it accelerates. The reaction force is on your foot and this causes your foot to decelerate. ▫ Think about kicking a kettle bell or medicine ball instead, does your foot now feel the deceleration?

Apparent Weight Weight or F g is due to gravity pulling down on a mass. Apparent weight is when the force of gravity has changed (temporarily) in such situations as traveling in an elevator. When the direction of acceleration is positive (ascending or stopping while going down), then your apparent weight is greater than your true weight. You “feel” heavier because the floor is pushing on you with a greater force than when elevator is stationary or moving at a constant velocity.

When the direction of acceleration is negative, (descending or slowing down while going up) then your apparent weight is less than your true weight. You “feel” lighter as the floor is falling out from beneath you.

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Free Falling Objects Recall that in the absence of air (friction), all objects fall with the same acceleration. When the the only force acting on the object is gravity, the object is said to be in free fall and its acceleration is equal to (-9.81 m/s 2 ). However, in air, there is an additional force acting on moving objects. This friction-like force is known as air resistance or the drag force.

Air resistance or drag force is the result of the moving object colliding with air molecules as it falls. The size of the drag force depends on the size and shape of the object, the density of the air, and the speed of the motion.

Dropping an Object Just after you drop an object, the force of gravity, Fg is larger than F drag so the object accelerates downward. As the velocity of object increases, so does the F drag. At some point, the F drag equals Fg so F net = 0, velocity becomes constant (no a)... this is known as the terminal velocity of the object. The value of terminal velocity depends on the shape and orientation of the object, the density if the air and the speed of motion. See Table 5.1

Momentum and Newton’s Laws We have stated that inertia was the resistance to any change in the position of an object, whether the object was at rest or in motion. Now, we will look at the inertia of moving objects which is known as momentum. Momentum ( ) is an effect created by the mass of an object traveling at a certain velocity. ▫ The product of the mass and velocity of a body. ▫ Vector quanitity with the same direction as the velocity of the object.

Momentum is not a force. Therefore, its units are not Newtons, instead they are. A single object with constant velocity and mass also has constant momentum, we say momentum is conserved. Do Model Problem on Page 197 Do Practice Problems # 29 on Page 197

Impulse Impulse ( ) is the product of a force and the time over which the force acts. ▫ A vector quantity with the same direction as the force. ▫ Units are N × s Do Model Problem on Page Do Practice Problems #s on Page 200

Impulse- Momentum Theorem The impulse-momentum theorem states that the impulse is equal to the change in momentum. It is another way of writing Newton’s 2 nd Law. Where - final momentum ( ) – inital momentum ( ) Or So

When you are playing sports you are trying to change the momentum as much as possible. To do this, you need to have a large impulse. You can get a large impulse by applying a large force for a short time or a smaller force for a long time. Ex. The longer you leave the bat in contact with the baseball, your foot on the football, or the racket on the tennis ball, the more you can increase the momentum. This idea is known as ‘follow-through’, but in physics we call it impulse.

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Chapter 5 Review Pages #s 34,

Force Worksheet Problems – Red Book Assignment Chapter 5 Review Dynamics Test 2