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## Warm-Up

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**Warm-Up**• Write down everything you know about force. Things you may want to include: • Definition • Formula • SI Units • Examples**Forces in One Dimension**Chapter 4**Force**• A force is a push or pull • Forces are vectors • Represented by “F” • Has SI units of Newtons • When all forces on an object are added, the result is called a net force. • A non-zero net force causes an acceleration**Special Types of Forces**• Fg: Force of gravity; weight – down towards center of Earth • FN: Normal force – perpendicular to surface object is on • Ff: Friction – opposes motion when two surfaces slide against each other • FT: Tension – in direction of string/rope/chain • Fdrag: Drag – opposes motion when an object moves through a gas or liquid (i.e. air resistance)**Vector Review**• Vectors have a magnitude and direction • Vectors can be depicted by an arrow • When drawing multiple vectors, their arrow lengths should be proportional to the vector magnitudes**Free Body Diagrams**• Draw a dot to represent the object • Draw an arrow for each force on the object • Arrows should start at the dot and point away • Arrow lengths should be proportional to force magnitude. For unknown forces, estimate length • Label each arrow • Choose a direction to be positive and indicate it on the side of the diagram • If object is moving, have positive direction be in direction of motion.**Example 1**• A book is sitting at rest on a table. Draw a free-body diagram for the book.**Example 2**• A box is pushed along the floor at a constant speed. Draw a free body diagram for the box.**You-Try #1**• A rope lifts a bucket at a constant speed. Draw a free body diagram for the bucket.**You-Try #2**• A student is pushing against a table, but not hard enough to move it. Draw a free body diagram for the table.**Warm-Up: October 24, 2011**• Power Tower is a thrill ride at Cedar Point, the roller coaster capital of the world. At the beginning of the ride, it accelerates the riders upwards. Draw a free body diagram of a rider at the beginning of a Power Tower ride.**Adding Forces**• Same process as adding velocity vectors. • The vector sum is called the net force, Fnet**Example 3**• Two horizontal forces, 273 N and 131 N, are exerted on a canoe in the same direction. Draw a free body diagram and find the net horizontal force on the canoe. • Now imagine the same two forces are acting in opposite directions. Draw a free body diagram and find the net horizontal force on the canoe.**You-Try #3**• Al and Bob are playing tug-of-war (two teams pulling on a rope in opposite directions) against Chris and Dan. Al pulls with a force of 127 N, Bob pulls with a force of 93 N, Chris pulls with a force of 104 N, and Dan pulls with a force of 119 N. Draw a free-body diagram and calculate the net force on the rope.**Newton’s Laws**• An object at rest will stay at rest unless acted upon by a non-zero net force. An object in motion will stay in motion unless acted upon by a non-zero net force. • The acceleration of an object is equal to the net force acting on the object divided by the object’s mass. • For every force, there is an equal and opposite force.**Mass**• The amount of matter in an object. • Represented by “m” • SI unit of kilograms (kg)**Example 4**• The driver of a car hits the accelerator and causes a net force of 3.00 x 103 N. If the car has a mass of 1.70 x 103 kg, what is the resulting acceleration?**You-Try #4**• A chair is pushed with a force of 93 N, and experiences a friction force of 11 N. If the chair accelerates at 1.7 m/s2, what is the mass of the chair?**Assignment**• Free-Body Diagrams worksheet**Warm-Up: October 25, 2011**• A 2.5 kg rock is falling off the edge of a cliff. Gravity is pulling it down with a force of 24.5 N. There is a drag force of 7.0 N. Draw a free-body diagram, and solve for the acceleration of the rock.**Acceleration due to Gravity (g)**• Near surface of Earth, g = 9.8 m/s2 • You must memorize this number • An object in free fall will have this initial acceleration • The weight of an object is given by Fg = mg**Example 5**• A skydiver with a mass of 73 kg free-falls. At one point, he has an acceleration of 8.3 m/s2. What is the force due to air resistance at this point?**You-Try #5**• A rope is pulling a bucket of water out of a well. The bucket of water has a total mass of 25 kg. What must the tension force be in order to accelerate the bucket at 0.60 m/s2.**Warm-Up: October 26, 2011**• After a few seconds of falling, the drag force on a 50.0 kg skydiver is 490 N. Draw a free-body diagram of the skydiver and calculate the acceleration of the skydiver.**Balanced Forces**• Forces are balanced if there is no net force • For two forces in opposite directions, arrows should be the same length. • For multiple forces, sum of arrow lengths in opposite directions should be the same. • Results in a zero acceleration (Fnet=ma) in that direction • Zero acceleration constant velocity • That velocity could be zero (no motion)**Unbalanced Forces**• Forces are unbalanced if there is a non-zero net force. • Arrows are different lengths. • Results in an acceleration in the direction of the longer arrow.**Equilibrium**• If all forces are balanced (in both x and y directions), then the system is in equilibrium. • There is zero acceleration • Zero acceleration constant velocity • That velocity could be zero (no motion)**Terminal Velocity**• Fdrag = -Fg(Equal magnitudes, opposite directions) • Zero net force zero acceleration constant velocity • The fastest an object can free-fall**Warm-Up:October 28, 2011**• A crane attached to a chain is being lowered. If the crane has a mass of 105 kg and is accelerating downward at a rate of 2.45 m/s2, what is the tension force between the chain and crane?**Groupwork**• You will work in groups of 3-4 • Mr. Szwast will assign groups • Work on each problem together (DO NOT split up the work) • Each person should record their work and answers • Mr. Szwast will check each individual’s work during class • There will be some presentations of answers • The worksheet may be collected at any point in the future**Warm-Up: October 31, 2011**• Every Halloween at Caltech, undergrads drop pumpkins (frozen by liquid nitrogen) from the top of Millikan Library, 42 meters above the sidewalk below. Ignoring air resistance, how long does it take until the pumpkin smashes into the sidewalk?**Chapter 4 Groupwork**• Return to your groups • You have 15 minutes to finish • Presentations will follow • Mr. Szwast will choose which member(s) of your group will present**Review of Forces**• Fg: Force of gravity; weight – down towards center of Earth • FN: Normal force – perpendicular to surface object is on (not present if object is in air) • FT: Tension – in direction of string/rope/chain • Ff: Friction – opposite direction of motion or applied force • Fdrag: Drag – air resistance; opposite direction of motion**Example 6: Warm-Up 10-11-2010**• A sphere with a weight of 49 N is dropped off the top of a building. Ignore air resistance. Draw a free-body diagram. After 1.0 second, what is the sphere’s • Acceleration • Velocity • Distance**Homework Corrections**• DO NOT WRITE ON THE HANDOUT • Homework was scored out of 10 points (4 extra credit point possible) • If you earned less than 7, copy all problems, work, and answers and turn them in to receive 7 points • If you earned more than 7 points, correct what you missed on your paper. • After you finish, get groupwork from Mr. Szwast and correct what you missed with your group • TURN IN THE HANDOUT BEFORE YOU LEAVE**Warm-Up October 14/15, 2010**• An object near the surface of the earth is being acted on by only one force. • What must this force be? • In what direction is the force? • In what direction is the object accelerating? • Can we conclude in what direction the object is moving? • Assume the initial time, distance, and velocity are zero. After exactly 3 seconds, what is the object’s • Acceleration • Velocity • Distance**Warm-Up: October 18, 2010**• A sphere with a weight of 98 N is dropped off the top of a building. Ignore air resistance. Draw a free-body diagram. After 2.0 seconds, what is the sphere’s • Acceleration • Velocity • Distance**Warm-Up: October 19, 2010**• Draw a free body diagram showing all the forces that are acting on you right now.**Classwork: Free Body Diagrams**• You will work with one partner. • Your partner will be the person assigned to sit at the same table as you. • If there is nobody else at your table, Mr. Szwast will assign you a partner. • You will have about 25 minutes to complete the worksheet. • Random students will then be called to the board to draw each free body diagram. • You will turn the worksheet in before you leave.**Warm-Up: October 21/22, 2010**Define, in your own words, the following terms: • Balanced • Unbalanced • Equilibrium