PHYSICS 149: Lecture 7

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1 PHYSICS 149: Lecture 7 Chapter 2 28Tension Fundamental Forces Chapter Position and Displacement Lecture 7 Purdue University, Physics 149 1

2 ILQ 1 Which statement about frictional forces is not true? A) Frictional forces are contact forces parallel to the contact surface. B) When frictional forces act to resist motion, two surfaces slide across each other. C) Frictional forces are perpendicular to the surface of contact. D) Frictional forces always act opposite to the direction of motion. E) The frictional force is always proportional p to the normal force on an object. Lecture 7 Purdue University, Physics 149 2

3 Tension Definition: Magnitude of Contact Force between different segments of the string (or between an end and the object attached there) Example: P T NOTE: T can only ypull the other object T is the force on the left portion from the right portion T is the tension at point P Lecture 7 Purdue University, Physics 149 3

Tension At any point in the rope (or string, cable or chain), tension is the pulling force exerted on the rope on one side of the point by the rope on the other side.

4 Tension At any point in the rope (or string, cable or chain), tension is the pulling force exerted on the rope on one side of the point by the rope on the other side. At its two ends, tension is the pulling force exerted on the object attached to its ends by the ropes at the ends. Note that tension can pull but not push. =T 4 =T 1 =T 2 If the chain s weight is not negligible, T 1 > T 2 > T 3 > T 4. =T 3 For example, T 1 = T 4 + chain s weight. Lecture 7 Purdue University, Physics 149 4

5 Ideal Cord An ideal cord has NO MASS Consequence: the tension is the same at ALL POINTS along the cord. Lecture 7 Purdue University, Physics 149 5

Tension with Ideal Cord Ideal cord : a cord that has zero mass and thus zero weight In an ideal cord,

force that the cord exerts on the objects attached to its ends (as long as there is no external force on

Note: In many cases, the weight of a cord is negligibly small compared to the weight of the objects

6 Tension with Ideal Cord Ideal cord : a cord that has zero mass and thus zero weight In an ideal cord, (a) the tension has the same value at all points along the cord, and (b) the tension is equal to the force that the cord exerts on the objects attached to its ends (as long as there is no external force on the cord). Note: In many cases, the weight of a cord is negligibly small compared to the weight of the objects attached to its ends, and thus we may assume that it is an ideal cord. =T 1 =TT 4 =T 3 =T 2 If the chain s weight is negligible (ideal cord), T 1 = T 2 = T 3 = T 4. Lecture 7 Purdue University, Physics 149 6

Ideal Pulley Pulley: A pulley serves to change the direction of a

The tension of an ideal cord that runs through an ideal pulley is

7 Ideal Pulley Pulley: A pulley serves to change the direction of a tension force, and may also (in the case of multiple-pulley systems) change its magnitude. Ideal pulley : a pulley that has no mass and no friction. The tension of an ideal cord that runs through an ideal pulley is the same on both sides of the pulley (and at all points along the cord). T= =T Lecture 7 Purdue University, Physics 149 7

8 ILQ 2 Two blocks with the same mass are connected by a lightweight cord that runs through an ideal pulley, as shown. When released, the blocks will end up A) at their current heights. eg B) at the same height. C) with left block on the ground. D) with right block on the ground. Lecture 7 Purdue University, Physics 149 8

9 ILQ 3 A heavy ball hangs from a string attached to a sturdy wooden frame. A second string (same kind) is attached to the bottom of the ball. You pull down the lower string slowly and steadily. Which string will break first? A) the top one B) the bottom one C) at the same time, because the tension is the same D) depends on the weight of the ball Lecture 7 Purdue University, Physics 149 9

10 Details of ILQ3 FBD of ball: Equilibrium ΣF y = 0 T2 ΣF y = T top T bottom W = 0 T top = T bottom + W Thus, T top > T bottom W T1 T1 NOTE: this problem is useful for CHIP problem with incline The top one receives stronger tension, so it will break first. Therefore T2 = T1+W>T1 Lecture 7 Purdue University, Physics

11 Example: Tension Given conditions: Ideal cord Tension is same. Equilibrium Net force = ΣF i = 0 Lecture 7 Purdue University, Physics

12 Tension Determine the tension in the 6 meter rope if it sags 0.12 m in the center when a gymnast with weight 250 N is standing on it. F = 0 x-direction: ΣF = m a -T L cosθ + T R cosθ = 0 y T L = T R y-direction: ΣF = m a T L sinθ + T R sinθ -W = 0 2 T sinθ = W T = W/(2 sinθ) = 3115 Ν x θ 3 m tanθ = θ = m Lecture 7 Purdue University, Physics

13 Tension y T 1 T 2 W Θ = tan -1 (0.12/3.00) = θ x y tightrope θ 3.00 m.12 m x T 1x = T 1 cosθ T 2x = T 2 cosθ W x = 0 T 1y = T 1 sinθ T 2y = T 2 sinθ W y = 250 N x-component: ΣF x = 0 ΣF x = T 1x + T 2x = T 1 cosθ + T 2 cosθ = 0 T 1 =T 2 y-component: ΣF y = 0 ΣF y = T 1y + T 2y W = T 1 sinθ + T 2 sinθ W = 2 T 1 sinθ W = 0 T 1 = T 2 = W /(2 (2 sinθ) = 250 N / [2 sin(2.291 )] 291 )] = N Lecture 7 Purdue University, Physics

14 Example: A Two-Pulley System What is the tension of the rope? FBD for Pulley L Equilibrium ΣF y = T c + T c W= 0 T c = W /2 = 902 N Since tension is the same at all points along the cord C, the person s pulling force is equal to T c. Therefore, the person pulling the rope only needs to exert a force equal to half the engine s weight. W = Lecture 7 Purdue University, Physics

15 Pulley Example T How much is T? T =100 N Explain why 200 N Lecture 7 Purdue University, Physics

16 ILQ What can you say about the tensions T1 and T2 at the two ends of the cord? (W is the weight of the cord) A) T1 > T2 B) T2 > T1 C) T1=T2 D) depends NOTE: this is NOT an ideal cord! T1 W T2 Lecture 7 Purdue University, Physics

17 ILQ If the weight W=0 then the cord is ideal. Is it true that T1=T2? A) no, T1>T2 B) yes, because of 3 rd NL C) no, T1<T2 D) yes, because of 1 st NL T1 NOTE: this IS an ideal cord! T2 Lecture 7 Purdue University, Physics

18 Gravity Fundamental Forces Acts on particles (and objects) with mass Always attractive; recall Newton s law of universal gravitation Range: unlimited The weakest of the four fundamental forces Electromagnetism Acts on particles with electric charge Binds electrons to nuclei to form atoms, and binds atoms in molecules and solid Responsible for contact forces like friction and normal force Either attractive or repulsive Range: unlimited Much stronger than gravity, 2nd strongest of the four fundamental forces Lecture 7 Purdue University, Physics

19 Fundamental Forces The Strong Force Binds together the protons and neutrons in atomic nucleus (and also quarks in combinations) Very short range: ~10-15 m (about the size of an atomic nucleus) The strongest of the four fundamental forces The Weak Force Responsible for some types of radioactive decays, sunlight Shortest range: ~10-17 m 3rd strongest of the four fundamental forces Lecture 7 Purdue University, Physics

20 Fundamental Forces Gravity Strong nuclear force Weak nuclear force Electromagnetic force Lecture 7 Purdue University, Physics

21 Zero Net Force vs. Nonzero Net Force Net Force: the vector sum of all the forces acting on an object Zero Net Force (Ch 2) When a net force on an object is zero, the velocity (both direction and magnitude) of the object does not change. Newton s First Law of Motion Nonzero Net Force (from Ch 3) When a nonzero o net force acts on an object, the velocity of the object changes. That is, either the velocity s direction or magnitude changes, or both of direction or magnitude change. Relevant to Newton s Second Law of Motion Lecture 7 Purdue University, Physics

22 Motion in One Dimension -x 0 The variables are time and distance t = 0 start of observations at a point x 0 t = t end of the observations at a point x f +x Objects are in motion and velocity is (change in distance)/time Velocity can change => acceleration (change in velocity)/time All quantities except time are vectors but the vector nature is contained in whether the quantity is positive or negative Lecture 7 Purdue University, Physics

23 Position Vector To describe position, we need a reference point (origin), a distance from the origin, and a direction from the origin. object at (x,y) Position Vector (or Position) A vector quantity that t consists of the distance and direction An arrow starting at the origin and ending with the arrowhead on the object Position vector is usually denoted by r. The x-, y-, and z- component of r are usually written simply as x, y, and z (instead of r x, r y, and r z ). Lecture 7 Purdue University, Physics

24 Position A vector quantity describing where you are relative to an origin Point A is located at x=3, y=1 or (3,1) Point B is located at (-1,-2) The vector r A indicating the position of A starts at tthe origin i and terminates t with arrowhead A Same for r B and B -3 Lecture 7 Purdue University, Physics B y 3-3 A 3 x

25 Distance vs. Displacement Distance (scalar) Total length of path traveled The path of an object does matter Displacement (vector) The change of the position vector ( r), that is, the final position vector (r f ) minus the initial position vector (r i ) = r f + ( r i ) An arrow starting at the initial position (the tip of the initial position vector) and ending with the arrowhead at the final position (the tip of the final position vector) The path of an object does not matter. The displacement depends d only on the starting ti and ending points. Lecture 7 Purdue University, Physics

26 Displacement (m) A vector quantity describing a change in position r = r f - r i The displacement from A to B is We can determine the components x-direction: x f -x i = -1 3 = -4 y-direction: y f -y i = -2 1 = -3 r = (-4, -3) r = sqrt( ) = 5 NOTE: The displacement is not the distance traveled -3 B y 3-3 A 3 x Lecture 7 Purdue University, Physics

Physics 101 Lecture 5 Newton`s Laws

Physics 101 Lecture 5 Newton`s Laws Dr. Ali ÖVGÜN EMU Physics Department The Laws of Motion q Newton s first law q Force q Mass q Newton s second law q Newton s third law qfrictional forces q Examples