1. Lecture 6 Newton’s Laws and Forces Sir Issac Newton (1642-1727)

2. l Agenda:  Recognize different types of forces and know how they act on an object in a particle representation  Identify forces and draw a Free Body Diagram  Solve 1D and 2D problems with forces in equilibrium and non-equilibrium (i.e., acceleration) using Newton’ 1 st and 2 nd laws.  Know what an IRF is and how it relates to Newton’s Laws

3. What causes motion? (Actually changes in motion) What are forces ? What kinds of forces are there ? How are forces and changes in motion related ?

4. Dynamics l Principia Mathematica published in 1687. This revolutionary work proposed three “laws” of motion: Law 1: An object subject to no net external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. FFa Law 2: For any object, F NET =  F = ma Important: Force is a vector and this is a vector sum FF Law 3: Forces occur in pairs : F A, B = - F B, A So…What is a force and how do we know it is there?

5. Force l We have a general notion of forces is from everyday life. l In physics the definition must be precise.  A force is an action which causes a body to accelerate. (Newton’s Second Law) Examples: Contact ForcesField Forces (Non-Contact) (physical contact (action at a distance) between objects) Kicking a ballMoon and Earth l On a microscopic level, all forces are non-contact

6. Gravity Newton also recognized that gravity is an attractive, long-range force between any two objects. When two objects with masses m 1 and m 2 are separated by distance r, each object “pulls” on the other with a force given by Newton’s law of gravity, as follows:

7. Cavendish’s Experiment F = m 1 g = G m 1 m 2 / r 2 g = G m 2 / r 2 If we know big G, little g and r then will can find m 2 the mass of the Earth!!!

8. Mass l We have an idea of what mass is from everyday life. l In physics:  Mass (in Phys 212) is a quantity that specifies how much inertia an object has (i.e. a scalar that relates force to acceleration) (Newton’s Second Law) l Mass is an inherent property of an object. l Mass and weight are different quantities; weight is usually the magnitude of a gravitational (non-contact) force. “Pound” (lb) is a definition of weight (i.e., a force), not a mass!

9. Inertia and Mass l The tendency of an object to resist any attempt to change its velocity is called Inertia l Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity (acceleration) If mass is constant then If force constant  l Mass is an inherent property of an object l Mass is independent of the object’s surroundings l Mass is independent of the method used to measure it l Mass is a scalar quantity l The SI unit of mass is kg |a| m

10. Newton’s First Law and IRFs inertial reference frame (IRF) An object subject to no external forces moves with a constant velocity if viewed from an inertial reference frame (IRF). If no net force acting on an object, there is no acceleration. l The above statement can be used to define inertial reference frames.  An IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”.  The surface of the Earth may be viewed as an IRF

11. Newton’s Second Law The acceleration of an object is directly proportional to the net force acting upon it. The constant of proportionality is the mass. l This expression is vector expression: F x, F y, F z l Units The metric unit of force is kg m/s 2 = Newtons (N) The English unit of force is Pounds (lb)

12. Newton’s Third Law: If object 1 exerts a force on object 2 (F 2,1 ) then object 2 exerts an equal and opposite force on object 1 (F 1,2 ) F 1,2 = -F 2,1 IMPORTANT: Newton’s 3 rd law concerns force pairs which act on two different objects (not on the same object) ! For every “action” there is an equal and opposite “reaction”

13. Exercise 1 A. 4 x as long B. 2 x as long C. 1/2 as long D. 1/4 as long A constant force is exerted on a cart that is initially at rest on an air table. The force acts for a short period of time and gives the cart a certain final speed s. Air Track Cart Force In a second trial, we apply a force only half as large. To reach the same final speed, how long must the same force be applied (recall acceleration is proportional to force if mass fixed)?

14. Solution Air Track Cart Force (B) 2 x as long F = ma Since F 2 = 1/2 F 1 a 2 = 1/2 a 1 We know that under constant acceleration, v = a  t So, a 2  t 2 = a 1  t 1 we want equal final velocities 1/2 a 1 /  t 2 = a 1 /  t 1  t 2 = 2  t 1

15. Exercise 2 A. 8 x as far B. 4 x as far C. 2 x as far D. 1/4 x as far A force of 2 Newtons acts on a cart that is initially at rest on an air track with no air and pushed for 1 second. Because there is friction (no air), the cart stops immediately after I finish pushing. It has traveled a distance, D. Air Track Cart Force Next, the force of 2 Newtons acts again but is applied for 2 seconds. The new distance the cart moves relative to D is:

16. Solution Air Track Cart Force (B) 4 x as long We know that under constant acceleration,  x = a (  t) 2 /2 (when v 0 =0) Here  t 2 =2  t 1, F 2 = F 1  a 2 = a 1