Lecture 6. Newton s laws of motion. Important note: First Exam is on Tuesday, Feb. 6, 8:15-9:45 pm

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1 Lecture 6 Newton s laws of motion Important note: First Exam is on Tuesday, Feb. 6, 8:15-9:45 pm

2 Today s Topics: Newton s Laws of Motion Newton s 1 st Law (Inertial reference frames) Vector nature of forces Newton s 2 nd Law Newton s 3 rd Law

3 Newton s First Law An object continues in a state of rest or in a state of motion at a constant velocity along a straight line, unless compelled to change that state by a net force. Sometimes referred to as Newton s Law of Inertia The net force is the vector sum of all of the forces acting on an object. Example forces: push, pull, gravity. DEMO: Air table

4 Inertia refers to the natural tendency of an object to remain at rest or in motion at a constant velocity along a straight line. The mass of an object is a quantitative measure of inertia. SI Unit of Mass: kilogram (kg) The unit of force is the Newton (kg m/s 2 )

5 Inertial Reference Frames An inertial reference frame is one in which Newton s law of inertia is valid. All accelerating reference frames are noninertial. Noninertial reference frames give rise to pseudoforces -Force you feel when a car accelerates -Weight you gain when an elevator starts rising Are we sitting in an inertial reference frame?

6 1) Force is a vector! å F = å Fx xˆ + å F y yˆ F x and F y must separately sum to 0 - F xˆ 2 2) We are only interested in those Forces that act on the object in question Object at rest: Nˆ y F xˆ 1 x ˆ : F xˆ - F ˆ 2x 1 = We define the weight of an object to be: 0 table -Wˆ y where m is the mass of the object. y ˆ : Nyˆ -Wyˆ = 0

7 Newton s Second Law - m acts as a measure of the inertia of an object - For a given net force, if m increases, a decreases DEMO: Air track

8 ACT: Sliding puck A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? a) more than its weight b) equal to its weight c) less than its weight but more than zero d) depends on the speed of the puck e) zero The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck. Follow-up: Are there any forces acting on the puck? What are they?

9 ACT: Sliding book You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? a) a net force acted on it b) no net force acted on it c) it remained at rest d) it did not move, but only seemed to e) gravity briefly stopped acting on it The book was initially moving forward (because it was on a moving bus). When the bus stopped, the book continued moving forward, which was its initial state of motion, and therefore it slid forward off the seat. Follow-up: What is the force that usually keeps the book on the seat?

10 ACT: No friction Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart? a) slowly come to a stop b) continue with constant acceleration c) continue with decreasing acceleration d) continue with constant velocity e) immediately come to a stop After the cart is released, there is no longer a force in the x-direction. This does not mean that the cart stops moving!! It simply means that the cart will continue moving with the same velocity it had at the moment of release. The initial push got the cart moving, but that force is not needed to keep the cart in motion.

11 ACT: Forces and blocks A force F acts on mass m 1 giving acceleration a 1. The same force acts on a different mass m 2 giving acceleration a 2 = 2a 1. If m 1 and m 2 are glued together and the same force F acts on this combination, what is the resulting acceleration? a) ¾a 1 b) 3 / 2 a 1 c) ½a 1 d) 4 / 3 a 1 e) 2 / 3 a 1 F F F a m1 1 m 2 F = m 1 a 1 a 2 = 2a 1 F = m 2 a 2 = (1/2 m 1 )(2a 1 ) m 2 m 1 a 3 Mass m 2 must be ( m 1 ) because its acceleration was 2a 1 with the same force. Adding the two masses 3 together gives ( )m 1, leading to an 2 acceleration of ( )a 1 for the same applied force F = (3/2)m 1 a 3 => a 3 = (2/3) a 1

12 The vector nature of forces 3 N 5 N! 37 4 N Individual Forces Net Force

13 How do I figure out the net force? The net force in this case is: 275 N N 560 N = +110 N and is directed along the + x axis of the coordinate system.

14 Example Two forces act on a 4.5-kg block resting on a frictionless surface as shown. What is the magnitude of the horizontal acceleration of the block? (a)1.8 m/s 2 (d)3.2 m/s 2 (b)1.2 m/s 2 (e)8.9 m/s 2 (c)0.82 m/s 2 +y 5.9N 3.7N 43 +x 3.7 N 5.9 N! F 1 = F 1x ˆx + F 1y ŷ = 3.7Nˆx + 0Nŷ! F 2 = F 2 x ˆx + F 2 y ŷ 43 = 5.9N cos(43 ) ˆx + 5.9N sin(43 )ŷ = 4.3Nˆx + 4.0Nŷ F x = F 1x + F 2 x = 3.7N + 4.3N = 8.0N a x = F + F m 8.0N 4.5kg 1 x 2x = = 1.8 m/s 2

15 Newton s Third Law And everyone s favorite! Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.

16 Why is this important? - F xˆ 2 Nˆ y F xˆ 1 table -Wˆ y The Normal force is a reaction force

17 Conceptual Problem If How can one team win a tug-of-war? F! 21 F! !! If F 21 > F Ground on 1 Team 2 wins! F! Groundon1 F! Ground on 2

18 When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? ACT: Climb the rope a) this slows your initial velocity, which is already upward b) you don t go up, you re too heavy c) you re not really pulling down it just seems that way d) the rope actually pulls you up e) you are pulling the ceiling down When you pull down on the rope, the rope pulls up on you!! It is actually this upward force by the rope that makes you move up! This is the reaction force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton s Third Law.

19 ACT: Horse and cart I A horse pulls a cart along a flat road. Consider the following four forces that arise in this situation. (1) the force of the horse pulling on the cart (2) the force of the cart pulling on the horse (3) the force of the horse pushing on the road (4) the force of the road pushing on the horse Which two forces form an "action-reaction" pair that obeys Newton's third law? (a) 1 and 4 (b) 2 and 4 (c) 2 and 3 (d) 1 and 3 (e) 3 and 4 CART F 1 F 2 F 4 HORSE F 3 ROAD

20 ACT: Horse and cart II Suppose that the horse and cart have started from rest; and as time goes on, their speed increases in the same direction. Which one of the following conclusions is correct concerning the magnitudes of the forces mentioned above? (a) (Action-reaction pair) (a) Force 1 exceeds force 2. (b) Force 3 exceeds force 4. (b) (Action-reaction pair) (c) Forces 1 and 2 cannot have equal magnitudes. (c) (Action-reaction pair) (d) Force 2 exceeds force 4. (d) (They would move in other direction) (e) Force 2 is less than force 3. (e) (Since F 4 = -F 3 then F 4 > F 2 and life is good) CART F 1 F 2 F 4 HORSE (1) the force on the cart by the horse (2) the force on the horse by the cart (3) the force on the road by the horse (4) the force on the horse by the road F 3 ROAD

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