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1 Lec 11 Return Exam1 Intro Forces Tuesday, February 19, :52 PM Exam 1 Stats: Average: 60% Approximate letter grade? Add 10%-12% (This is not a curve) This takes into account the HW, Lab, and Grade Replacement. Interpreting a velocity function: (Ver A: 20-22, Ver B: 10-12) The accel is +, the velocity is -, Since they are opposite, the object is slowing down. Person 2 m/s constant-v, 3 m/s, for the same distance. What is average speed? Adding displacements: Lec 11 Return Exam1, Intro Forces Page 1

2 Lec 11 Return Exam1, Intro Forces Page 2

3 Exam 1 Projectile - Max Range Tuesday, February 19, :32 PM A-11 or B-14: Both velocity and accel are negative. Speeding up Lec 11 Return Exam1, Intro Forces Page 3

4 Lec 11 Return Exam1, Intro Forces Page 4

5 Next Topic: Dynamics and Forces Tuesday, February 19, :50 PM (Chap 4 on Newton's Laws) Dynamics is the study of how to affect the motion of objects. The most basic cause of motion is the force. Any push, pull, or drag qualifies as a force. A force is an attempt to affect the motion of an object. The attempt could fail because of other forces. "affecting the motion" refers to changing the motion. Objects naturally maintain any motion they have. Could be trying to move a stationary object. Could be trying to slow or stop a moving object. Could be trying to deflect or bend the path of an object. It is the net force or total force that matters. The net force actually causes the acceleration of the object. Every force exists in two "copies" that are equal and opposite. Lec 11 Return Exam1, Intro Forces Page 5

6 Lec 12 Forces Thursday, February 21, :58 PM The net force acting on an object causes its acceleration. Must add forces. For every force, there is an object that "feels" the force. There is another object that "causes" the force. But, the objects can always switch places to be part of another "copy" of the original force. There is also a "mechanism" or reason for the force. Example: Object on a Table Normal force: Must push, but can be any strength. Is always perpendicular to the surface. Gravity force: Always points down. Strength is proportional to object mass. It's pretty common for the normal force to equal the weight of the object. What must be true? Accel must be zero. Only two vertical forces. Normal force must be vertical. Lec 12 Forces Page 6

7 Only two vertical forces. Normal force must be vertical. Force Analysis of the Table The floor must hold up both the table and the box. What does acceleration do to the Normal force? If the accel is upward (+), F_N must be greater than the weight. If the accel is down (-), F_n must be weaker than the weight. Lec 12 Forces Page 7

8 Lec 12 Forces Page 8 Types of Forces Thursday, February 21, :46 PM To build a list of forces, it's nice to have a checklist. I use the force mechanisms to figure out what forces exist. Distance forces (what's not touching the object?) Gravity Electromagnetic Contact forces (what is touching the object?) Fluid forces: Static pressure, drag, buoyancy Solid forces: Normal force (pushing, repulsive) Friction force (dragging, shear) Tension (pulling, attractive)

9 Incline - Object at rest Thursday, February 21, :53 PM If I use x-y components: When drawing friction, it can be along the surface in either direction (uphill or downhill). Friction fights the slide. This box tries to slide downhill (b/c gravity), so friction points uphill to fight that. Use a tilted coordinate system: Since F_g is theta from the y-axis, cos(theta) goes in the y-equation. Lec 12 Forces Page 9

10 Lec 13 Friction Tuesday, February 26, :58 PM If the object starts from rest, a gentle pull won't move it. Friction is along the surface, opposing sliding. It's as strong as it needs to be (within a limit). Here is our model of how strong friction is allowed to be: Typical friction coefficients: Note this is not a formula for the static friction force. How much pulling force is needed to overcome static friction? Lec 13 Friction Page 10

11 This says as long as F_P is less than 245 N, static friction can maintain grip. Lec 13 Friction Page 11

12 Static Friction with a self-propelled object Tuesday, February 26, :21 PM It is the static friction force that provides forward, motivating force. The actual amount of friction is controlled by the driver. We can say the maximum amount. Braking is the same story, but with friction pointing backward. Ex: Lec 13 Friction Page 12

13 Lec 13 Friction Page 13

14 Max friction on an Incline Tuesday, February 26, :37 PM In an inequality, be careful about dividing by a negative. Here, cos(theta) is positive because theta is 1st quadrant. Lec 13 Friction Page 14

15 Kinetic Friction Tuesday, February 26, :49 PM Kinetic friction is friction of sliding. It opposes actual sliding. It has a value (instead of a limit) It is weaker than maximum static friction. mu_k theta accel Ignore negative values Lec 13 Friction Page 15

16 Pulling a sled at an angle Tuesday, February 26, :04 PM Pulling 10 degrees, we only need 229 N to move the sled. 0 degrees, we needed 245 N. Lec 13 Friction Page 16

17 Lec 14 Connected Objects Thursday, February 28, :54 PM Draw separate diagrams. String 1 does 2 things: F_T1 on each box. Accel is same for each box. This equation looks like it models this diagram: Only the external forces matter in this diagram. This is the System Approach. But what's the tension in the middle string? Must model just one object. Lec 14 Connected Objects Page 17

18 Three different force diagrams and equations: Two independent masses. One system diagram. Only external forces matter. Lec 14 Connected Objects Page 18

19 Atwood's Machine Thursday, February 28, :26 PM Separate force diagrams: The string links the motions of the two objects. Extreme cases: Lec 14 Connected Objects Page 19

20 Lec 14 Connected Objects Page 20

21 Half-Atwood Machine Thursday, February 28, :43 PM System approach, external forces in the direction of motion: Other important equations: What is the tension? Lec 14 Connected Objects Page 21

22 What is the tension? Lec 14 Connected Objects Page 22

23 Lec 15 Circular Motion Monday, March 4, :20 AM Textbook Sections and 7.4. Constant Velocity Motion Speeding up along a Line To speed up, accel must be in the same direction as the motion. Circular Motion The acceleration points "inward" toward the center of the circular motion. This is centripetal acceleration. Magnitude of centripetal accel: Ex: Entrance road to campus Force diagram for the car: Lec 15 Circular Motion Page 23

24 Force diagram for the car: As long as the static coefficient is more than 0.15, we're okay. Lec 15 Circular Motion Page 24

25 Vertical Circles - Changing the Normal Force Tuesday, March 5, :30 PM The normal force must be less than the weight. The normal force must be pushing. Its minimum is zero. This gives us a maximum speed for driving over the hill. Let's try to design a speed hump. Lec 15 Circular Motion Page 25

26 Looping Around Tuesday, March 5, :47 PM The normal force vector must be downward, which means the F_N variable must be +. This sets a minimum speed at the top. What does the situation look like at the bottom of the loop? No special requirements. F_N is more than the weight. Lec 15 Circular Motion Page 26

27 Fictitious Forces Tuesday, March 5, :00 PM When we sit in a chair, we feel pressed down into the chair. What we're actually feeling is the chair pressing up against us. When sitting in a car that slams on the brakes, we feel thrown forward. What's actually happening is the car pushes back on us to slow us. It's our inertia that tries to make us keep going forward. When in a car that is accelerating, we feel pressed back into the seat. What's actually happening is the car pushes us forward. Our own inertia tries to keep us from speeding up. When in a car that makes a right turn, we feel pushed toward the left. It's just our inertia trying to make us go in a straight line. The actual force is rightward, making us follow the curve. This sensation is so ubiquitous that it has a name: centrifugal force. Lec 15 Circular Motion Page 27

28 Lec 16 Buoyancy Monday, March 4, :28 AM Textbook Section 9.5 Buoyancy is a static force caused by being immersed in a fluid. The direction is always upward. The strength is the weight of the displaced fluid. Weight of any object: Density of a material: Weight of a hunk of material: Buoyant Force: Three free-body diagrams for buoyancy: (all static = equilibrium) Lec 16 Buoyancy Page 28

29 Floating Object Thursday, March 7, :22 PM Typical description: A floating object has 5% of its volume above the surface. The fluid is distilled water. What is the object density? If I float the same object in seawater ( ), How much will be above the surface? Lec 16 Buoyancy Page 29

30 Sunken objects Thursday, March 7, :34 PM A hunk of material is hung from a string. While hanging in air, the tension is 98 N When dunked in water, the tension is 93 N. How can we figure out the density of the object? Lec 16 Buoyancy Page 30

31 Cargo on a Boat Thursday, March 7, :46 PM Typical barge: How much coal (in kg) makes the barge drop by 10 cm? It takes 65 metric tons to make the boat lower by 10 cm. Lec 16 Buoyancy Page 31

32 Lec 17 Torque and Balance Tuesday, March 19, :53 PM Exam 2 Thu 3/28: Forces, Circular Motion, Torque (Don't forget Kinematics) Torque - Like force, but for rotations. Torque is any attempt to rotate or restrict the rotation of an object. Torque is a side-effect of almost every force. What affects the amount of the torque? The force strength. The amount of leverage. The relative direction of the force. Torque formulas: Torque (tau) is measured in newton-meters (N m). Ex: Torque of a tension force: Alternate formula: Lec 17 Torque and Balance Page 32

33 Net Torque and Equilibrium Tuesday, March 19, :25 PM Newton's Second Law versions: Example: See-saw or balance. Free body Diagram: Let's say a 30 kg child is m1, 2.0 m from the pivot. A 60 kg adult is baby sitting and wants to balance. Where should they sit? Lec 17 Torque and Balance Page 33

34 To balance, the more massive object must have less leverage. Lec 17 Torque and Balance Page 34

35 Banner Post Tuesday, March 19, :47 PM A 2 m long post is used to hold up a 10 kg sign that is centered 1.7 m from a wall. A rope is tied to the end of the sign and attached to the wall 0.75 m above the post. What is the tension in the rope? Note: Lec 17 Torque and Balance Page 35

36 Lec 18 Static Equilibrium Thursday, March 21, :56 PM To remain at rest, both forces and torques on an object must balance. Ex: Sharing the Load. A 100 kg, 4.0 m long beam is carried by two people. Person A is at one end, Person B is 0.5 m from the other end. How much force must each person provide? By picking the pivot point at the location of one unknown force: F_A wasn't cluttering up our torque equation. We couldn't directly find F_A from the torque equation. What if we had chosen the middle as the pivot point? Lec 18 Static Equilibrium Page 36

37 Falling Can Thursday, March 21, :25 PM If the can *does* have a bottom, the lower ball exerts a downward force that holds the can in place. Lec 18 Static Equilibrium Page 37

38 Leaning Ladder Thursday, March 21, :36 PM A 4.0 m ladder leans against a frictionless wall. The coefficient of friction with the floor is 0.3. What angle can the ladder have with the floor and not fall over? This is the threshold angle. Is it okay for theta to be more or less? More is okay here. When using measure d perpendicular to the force. Lec 18 Static Equilibrium Page 38

39 Classes of Levers Thursday, March 21, :53 PM A lever is a strong, lightweight beam that we apply a force to, in order to exert some other load force. Levers are classified by where the forces and pivot are. Class 1 Lever: Pivot in the middle The applied and load forces (on the lever) are in the same direction. The lever exerts an opposite force onto the load. This is the "output" force. Class 2 Lever: Load in the middle Ex: Wheelbarrow. The applied force is weaker because it has more leverage. Class 3 Lever: Applied force in the middle. The applied force must be stronger because it is at a "mechanical disadvantage". Ex: Biceps muscle acting on forearm. Lec 18 Static Equilibrium Page 39

40 Lec 19 Review Tuesday, March 26, :57 PM Exam 2 Thursday: Forces, Circular Motion, Torque Note: Spring 2018 Practice Exam doesn't have Circular Motion. In intro physics, circle is either vertical or horizontal. Ex: Horizontal circle, driving around a bend: Ex: Driving 30 m/s, with friction coefficient 0.5, what radius of curvature is achievable? Vertical circle: Gravity is vertical. Usually gravity and some other force together cause the centripetal acceleration. A 4.0 m long rope has a tire hanging at the end. The tire weighs N. How fast would it have to go in order for the tension in the rope to be N? Lec 19 Review Page 40

41 Lec 19 Review Page 41

42 Buoyancy Tuesday, March 26, :27 PM Ex: Floating object with 10% above the surface. If fluid is water: If we put the same object into salt water with The fraction must change: Also review how to find density of "heavy" object with two "weighings". Lec 19 Review Page 42

43 Atwood's Machines Tuesday, March 26, :42 PM How could we get the most accel? How could we get the least accel magnitude? If m1 = 5 kg, and m2 = 10 kg, what's the tension? Lec 19 Review Page 43

44 Torque and Balance Tuesday, March 26, :55 PM Lec 19 Review Page 44

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