Newton’s Laws The Study of Dynamics

Isaac Newton Arguably the greatest scientific genius ever. Came up with 3 Laws of Motion to explain the observations and analyses of Galileo and Johannes Kepler. Discovered that white light was composed of many colors all mixed together. Invented new mathematical techniques such as calculus and binomial expansion theorem in his study of physics. Published his Laws in 1687 in the book Mathematical Principles of Natural Philosophy.

What is a Force? NO not THE Force A force is a push or pull on an object. It may be from gravity, electrical, magnetic, or muscle efforts. http://members.aol.com/PrinceG0R0/jedi.html

A net force causes an object to accelerate… To speed up To slow down To change direction

~Arise because of direct ~Gravity Contact Forces Field Forces ~Arise because of direct ~Gravity contact between objects. ~Electric Act over a distance. ex: friction, tension ~Magnetic

Free body diagram (FBD) Shows all the forces acting on an object. support force friction force Applied force weight

Newton’s First Law A body in motion stays in motion at constant velocity and a body at rest stays at rest unless acted upon by a net external force. This law is commonly referred to as the Law of Inertia.

Implications of Newton’s 1st Law If there is zero net force on a body, it cannot accelerate, and therefore must move at constant velocity, which means it cannot turn, it cannot speed up, it cannot slow down.

What is Zero Net Force? SF = 0 The table pushes up on the book. FT A book rests on a table. Physics Gravity pulls down on the book. FG Even though there are forces on the book, they are balanced. Therefore, there is no net force on the book. SF = 0

Diagrams Draw a force diagram and a free body diagram for a book sitting on a table. Physics N W Force Diagram N W Free Body Diagram

Sample Problem A monkey hangs by its tail from a tree branch. Draw an FBD representing all forces on the monkey FT FG

Sample Problem Now the monkey hangs by both hands from two vines. Each of the monkey’s arms are at a 45o from the vertical. Draw an FBD representing all forces on the monkey. Fa1 Fa2 FG

Mass and Inertia Chemists like to define mass as the amount of “stuff” or “matter” a substance has. In physics mass is a measure of inertia, which is the ability of a body to resist acceleration by a net force.

Demonstration A heavy block hangs from a string attached to a rod. An identical string hangs down from the bottom of the block. Which string breaks when the lower string is pulled with a slowly increasing force? when the lower string is pulled with a quick jerk? Top string breaks due to its greater force. Bottom string breaks because block has lots of inertia and resists acceleration. Pulling force doesn’t reach top string.

Newton’s Second Law A body accelerates when acted upon by a net external force. The acceleration is proportional to the net force and is in the direction which the net force acts.

Newton’s Second Law ∑F = ma where ∑F is the net force measured in Newtons (N) m is mass (kg) a is acceleration (m/s2)

Units of force Newton (SI system) 1 N = 1 kg m /s2 1 N is the force required to accelerate a 1 kg mass at a rate of 1 m/s2 1 N=.225 lb (about the weight of a stick of butter)

Working 2nd Law Problems Draw a free body diagram. Set up 2nd Law equations in each dimension. SFx = max and/or SFy = may Identify numerical data. x-problem and/or y-problem Substitute numbers into equations. “plug-n-chug” Solve the equations.

Sample Problem In a grocery store, you push a 14.5-kg cart with a force of 12.0 N. If the cart starts at rest, how far does it move in 3.00 seconds?

Sample Problem A catcher stops a 92 mph pitch in his glove, bringing it to rest in 0.15 m. If the force exerted by the catcher is 803 N, what is the mass of the ball?

Sample Problem A 747 jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is 3.50 x 105 kg, its speed is 27.0 m/s, and the net braking force is 4.30 x 105 N a) what is its speed 7.50 s later? b) How far has it traveled in this time?

Newton’s Third Law For every action there exists an equal and opposite reaction. If body A exerts a force F on body B, then body B exerts a force of -F on body A.

Examples of Newton’s 3rd Law

Sample Problem You rest an empty glass on a table. a) How many forces act upon the glass? b) Identify these forces with a free body diagram. c) Are these forces equal and opposite? d) Are these forces an action-reaction pair? Identify the action-reaction force pairs.

Sample Problem A force of magnitude 7.50 N pushes three boxes with masses m1 = 1.30 kg, m2 = 3.20 kg, and m3 = 4.90 kg as shown. Find the contact force between (a) boxes 1 and 2 and (b) between boxes 2 and 3.

Mass and Weight Many people think mass and weight are the same thing. They are not. Mass is the amount of matter in an object, measured by its inertia, or resistance to acceleration. Weight can be defined as the force due to gravitation attraction. W = mg

Sample Problem A man weighs 150 pounds on earth at sea level. Calculate his a) mass in kg. b) weight in Newtons.

Apparent weight If an object subject to gravity is not in free fall, then there must be a reaction force to act in opposition to gravity. We sometimes refer to this reaction force as apparent weight.

Elevator rides When you are in an elevator, your actual weight (mg) never changes. You feel lighter or heavier during the ride because your apparent weight increases when you are accelerating up, decreases when you are accelerating down, and is equal to your weight when you are not accelerating at all.

Going Up? v = 0 a = 0 v > 0 a > 0 v > 0 a = 0 v > 0 W Wapp Ground floor Normal feeling v = 0 a = 0 W Wapp Just starting up Heavy feeling v > 0 a > 0 W Wapp Between floors Normal feeling v > 0 a = 0 W Wapp Arriving at top floor Light feeling v > 0 a < 0 Going Up?

Going Down? v = 0 a = 0 v < 0 a < 0 v < 0 a = 0 v < 0 Wapp Top floor Normal feeling v = 0 a = 0 W Wapp Beginning descent Light feeling v < 0 a < 0 W Wapp Between floors Normal feeling v < 0 a = 0 W Wapp Arriving at Ground floor Heavy feeling v < 0 a > 0 Going Down?

Sample Problem An 85-kg person is standing on a bathroom scale in an elevator. What is the person’s apparent weight a) when the elevator accelerates upward at 2.0 m/s2? b) when the elevator is moving at constant velocity between floors? c) when the elevator begins to slow at the top floor at 2.0 m/s2?