Introduction to Newton s Laws Newton s First Law. 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. 1
What is Force? A force is a push or pull on an object. Forces cause an object to accelerate > To speed up > To slow down > To change direction 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. 2
The First Law is Counterintuitive Aristotle firmly believed this. But Physics 1 students know better! 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. 3
Free Body Diagram a picture that shows all the forces acting on an object where all forces originate a single point at the center of the object (the center of mass). Misconception Alert: This type of diagram applies only to translational motion and not rotational motion (we will examine rotation in another unit) Free Body Diagram of a book at rest on a table Free Body Diagram of a book sliding at a constant velocity on a table Oct 30 11:22 AM Sample Problem A monkey hangs by its tail from a tree branch. Draw a free body diagram representing all forces on the monkey FT FG 4
Sample Problem Now the monkey hangs by both hands from two vines. Each of the monkey s arms are at a 45 o from the vertical. Draw a force diagram representing all forces on the monkey. Fa1 Fa2 FG Newton s Second Law 5
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 Σ F = ma where Σ F is the net force measured in Newtons (N) m is mass (kg) this is inertial mass. a is acceleration (m/s 2 ) 6
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. It is approximately the force required to lift an apple or two. Pound (British system) > 1 lb = 1 slug ft /s2 Working 2nd Law Problems Draw a free body diagram. Set up X & Y chart to find 2 nd Law equations in each dimension. (F = ma) Forces Add the columns to get the Net Force in the x & y directions ΣF x = ma x and/or ΣF y = ma y Use Pyth. Theorem to solve for the Overall Net Force (Fnet) and the tan -1 (Fnet y / Fnet x) to get θ. F net x y ΣF x = ma x ΣF y = ma y 7
3 Forces act on a 20 kg object: F1 = 200 N at 35 degrees above the x, F2 = 50 N in +y, F3 = 150 N at 20 degrees below the +x. a) Determine the magnitude and direction of the net force for the situation. b) Find the acceleration of tjhe object (magnitude and direction). Oct 30 11:34 AM Newton s Third Law 8
Newton s Third Law For every action there exists an equal and opposite reaction. If A exerts a force F on B, then B exerts a force of -F on A. The pair of forces are known as an actionreaction pair. Examples of Newton s 3rd Law Copyright James Walker, Physics, 1st edition 9
Treating multiple objects as a SystemSample 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. Copyright James Walker, Physics, 1st edition Sample Problem An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the negative y direction. Find the direction and magnitude of the third force acting on the object. 10
Specific Forces 1. Weight or Gravity G 2. Normal N 3. Friction f 4. Tension T Oct 31 7:52 AM Misconception Alert Mass and Weight 11
Mass and Inertia Chemists like to define mass as the amount of stuff or matter a substance has. Physicists define mass as inertia, which is the ability of a body to resist acceleration by a net force. Mass and Weight Many people think mass and weight are the same thing. They are not. Mass is inertia, or resistance to acceleration. Weight can be defined as the force due to gravitation attraction. G = mg - gives you gravitational force 12
Normal Force Normal force The normal force is a force that keeps one object from penetrating into another object. The normal force is always perpendicular to a surface. The normal force exactly cancels out the components of all applied forces that are perpendicular to a surface. There is No formal equation for normal force, you have to determine it from the other forces acting on the object. 13
Ex: Normal force If the box has a mass of 5 kg, what is its weight (G)? What normal force is acting on the box? If I push downward on the box with 11 N of force, what is the normal force? If I pull up on the box with 11 N of force what is the normal force? Normal force not associated with weight. A normal force can exist that is totally unrelated to the weight of an object. applied force Wall 14
Normal force on ramp The normal force is perpendicular to angled ramps as well. Sample problem Find the normal force exerted on a 2.5 kg book resting on a surface inclined at 28 0 above the horizontal. If the angle of the incline is reduced, do you expect the normal force to increase, decrease, or stay the same? 15
Sample problem A gardener mows a lawn with an old fashioned push mower. The handle of the mower makes an angle of 32 degrees with the surface of the lawn. If a 249 N force is applied along the handle of the 21 kg mower, what is the normal force exerted by the lawn on the mower? What is the acceleration of the lawnmower? Friction Friction (f) force that attempts to counteract sliding 2 types: kinetic friction, fk, (object moving/sliding) & static friction, fs, (object at rest) For the same surfaces in contact: Static friction is always larger than kinetic friction. 16
Friction (cont.) Both utilize the same equation: f = μ N where μ is the coefficient of friction and is dependent upon the surfaces in contact. For most materials, μ < 1. Static friction is also a lazy force and does only as much as it has to, but it has a limit. Once a force is applied that is greater than static friction the object will move and kinetic friction will act on the object. Tension Tension (T) pulling force with in a cord, string or rope. It acts in both directions within the cord because of Newton s 3rd law. Ex: Think about dragging a box by a rope. You pull on the rope (Action) & the rope pulls on you (Reaction). Those forces are equal and opposite. 17
Atwood Problems mass attached by idealized strings with a pulley. Idealized = no friction, no mass, no stretching Nov 3 1:00 PM Solve for acceleration of blocks and tension in rope. How does the acceleration of each block compare? What values will the acceleration be between? How does the tension in the cord compare to the force of gravity acting on each block? What values will the tension be between? m b = 3 kg m c = 5 kg Nov 3 1:04 PM 18
Dec 15 2:48 PM Solve for the acceleration and tension m b = 0.21 kg m c = 0.20 kg Dec 10 8:20 AM 19
Oct 21 8:44 AM 20