9/23 Forces (2nd Law today) Text: Begin Chapter 4 Exam I key will be posted upstairs under “Exams” sometime today Discuss Exam I HW “9/23 2nd Law” due Thursday 9/26 Lab: “Forces and Acceleration” Study Buddies and Tutoring (peer instructors)

Road Map of this course 2nd law: Connects acceleration (not velocity) to a cause which is force. Ch 4 2nd law applies to curved motion. Ch 5 is Circular Motion 2nd law gets “messy” if the forces are sudden or change as time passes. (collisions, springs, etc.) Enter the concepts of Energy (springs) and Momentum (collisions) which are useful when the 2nd law gets messy. Ch 6 and 7 Rotating objects are covered in Ch 8 and 9

Fnet = ma Newton’s Second Law Says that the acceleration points in the exact same direction as the net force. Says that the acceleration is proportional to the net force. Says that the acceleration is inversely proportional to the mass. This is why the direction of the acceleration is such an important concept.

Newton’s Second Law in 1D Fnet = ma Two forces act on the block as shown by arrows. What is the magnitude and direction of the net force? 8N 6N Adding these two together gives a net force vector of length 2N that points left. Fnet = 2 left

Newton’s Second Law in 1D Fnet = ma Two forces act on the block as shown by arrows. What is the magnitude and direction of the net force? 8N 6N Fnet = 2N left If the mass is 2kg, what is the acceleration? a = 1m/s2 left

Your Homework How does the tension in string 1 compare to that of string 2? A B m 1 2

Your Homework How does the tension in string 1 compare to that of string 2 now that the carts are released? A B m 1 2

Your Lab Upon releasing the cart, things accelerate. Both objects have the same acceleration magnitude, but different acceleration direction. The tension in the string is unknown, but is the same everywhere along its length in all cases. Moving mass from the cart to the suspended weight changes the acceleration. a cart TS,M WE,M = mg T < W 2nd law TS,C a mass

Your Lab You will make several runs, moving mass from the cart to the hanging weight. (This keeps the “m” in Fnet = ma the same for each trial.) Each trial will have a different acceleration and a different hanging weight, but the same total mass. You will plot the “accelerating force” (WE,M) against the acceleration to check if the acceleration is indeed proportional to the net force. (That is, is your plot a straight line?) a cart TS,M WE,M = mg T < W a TS,C mass

Free Body Diagrams Free Body Diagrams: A picture of all the forces acting “on” a single object, none on other objects. A Free Body Diagram also identifies the object the force is caused “by.” (All forces have a real object as the cause) Normal force by the floor on Larry. NF,L Example: 1st subscript = “by” object 2nd subscript = “on” object This dot is Larry WE,L N = W by 2nd law This is the “Weight force” caused “by” the earth “on” Larry.

parallel to contact surface perpendicular to contact surface Types of Forces Noncontact Forces Contact Forces Gravitational Electromagnetic Nuclear Pushes (touch) Pulls (ropes) Electric Magnetic W Friction Normal Tension T M f N Note: The text uses FN , not N as we will. parallel to contact surface perpendicular to contact surface