Newton's Laws of Motion: Understanding Force, Inertia, and Acceleration - Prof. Costa P. G, Study notes of Physics

Download Newton's Laws of Motion: Understanding Force, Inertia, and Acceleration - Prof. Costa P. G and more Study notes Physics in PDF only on Docsity! 1 Chapter 5 Newton’s Laws of Motion Chapter 5: Newton’s Laws of Motion We will study classical motion: • No quantum mechanics • No relativity We introduce the concept of force and define it in terms of the acceleration of a “standard body” 2 Intuitively, we know that force is a “push” or “pull”. Forces come in different classes (types):
Contact
Macroscopic forces of contact friction, viscosity, the contact force from the floor supporting my feet).
Field (originally described as action-at-a-distance)
Examples: Gravity, Electromagnetism Force F is a vector quantity: You push or pull in a specific direction F If force has direction, what is it’s measure? The Empirical ‘Feel’ of Forces • We have a direct sensation of the forces that act on our body.
As I stand on the floor, I feel my shoes pushing up on my feet. The nerves in the soles of my feet transmit this feeling to my brain.
The nerves in our joints also give us a sense of the weight of our bodies.
If you hit your toe (or worse) you feel the force against your toe. 5 Inertia The tendency of an object to resist a change in its velocity is called inertia. The measure of inertia is mass.
SI units measure mass as multiples of the standard kilogram (kg=1000g) stored at the International Bureau of Weights and Measures in Sèvres, France. Newton’s First Law tells us about motion if F = 0 What if F ≠ 0? Newton’s Second Law The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. The direction of the acceleration is the direction of the resultant force. F = ma 6 FNet = ma Implicit and explicit meaning • Force is a vector
The net force is the vector sum of all forces acting on the object m. • Mass is a scalar:
The value of the mass of an object does not change with the direction of the acceleration. • Mass is invariant:
If two objects are put together (or separated) , the mass of the combined object is simply the arithmetic sum of the two masses m = m1+m2.
Chemical combination, welding, cutting does not change mass. • Einstein corrected this, but Relativistic effects are small for ordinary matter. • Force can be quantified by measuring the acceleration it produces on a standard kilogram (or any multiple there-of). An object of mass 5 kg undergoes an acceleration of [8 m/s2 ŷ] = 8 m/s2 in + y direction What is the force on that object? F = ma = (5 kg)(8 m/s2) ŷ = 40 kg⋅m/s2 ŷ ŷ = vector on unit length (no dimensions) in +y direction. The force is in the same direction as the acceleration. Example 7 Units The SI unit of Force is the Newton defined as: 1 N = 1 kg⋅m/s2 Notice pounds and kilograms do not directly convert. The British unit of mass is the slug (don’t ask). The force of gravity (near Earth’s surface) acting on a 1 kg mass is 2.2 lb.: (1.0 kg) (g) = 2.2 lb. Do not confuse g=gram with g=9.8m/s2=acceleration due to gravity. Problem 1 A catcher stops a 92 mi/h pitch in his glove, bringing it to rest (with uniform deceleration) in 0.15 m. If the force exerted by the catcher is 803 N, what is the mass of the ball? (1 mi =1609 m) 10 Problem 3 A farm tractor tows a 4400-kg trailer up a 21° incline at a steady speed of 3.0 m/s. What force does the tractor exert on the trailer? (Ignore friction.) Weight The weight of any object on the Earth is the gravitational force exerted on it by the Earth: W = mg Note: Weight is a force (and therefore a vector). Weight is not equivalent to mass. Can a person’s weight be zero? When we say we want to “lose weight”, what do we really mean? 11 Apparent Weight Our sensation of weight comes from the force of the floor pushing up on us. We can feel light or heavy if the floor is accelerating down or up. The upward force of the floor on our feet is known as apparent weight Wa. It is your apparent weight that is measured on a scale. As part of a physics experiment, you stand on a bathroom scale in an elevator. Though your normal weight is 610 N, the scale at the moment reads 730 N. (a) Is the acceleration of the elevator upward, downward, or zero? (b) Calculate the magnitude of the elevator’s acceleration. Problem 4 12 Normal Forces Normal means perpendicular. table box N The normal force is a contact force and is perpendicular to the surface between the two objects in contact. The table and the box are compressing each other’s atoms slightly, like springs. The box pushes down on the table and the table pushes up on the box. These two forces are reaction pairs. -N If you lean against the wall, the normal force from the wall is horizontal. When the cart rolls down the incline in your physics lab, the normal force is perpendicular to the incline Motion on an Incline Frictionless • Cart rolls without friction on incline • Find the acceleration of the cart (as a function of θ). • Draw a coordinate system parallel to incline • x,y-components of gravity
Wx = -mg sin(θ)
Wy = -mg cos(θ) θ Free Body Diagram x y N mg N mg -y θ-x or