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AP Physics – Newton’s Laws – Force and Motion Types of Forces Contact forces: Sample Problem: Three forces act upon a 3.0 kg body moving at constant velocity. F1 = (4i – 6j +k) N and F2 = (i – 2j - 8k) N. Find F3. Field forces: Equilibrium Definition: Sample Problem: Two forces, F1 = (4i – 6j + k) N and F2 = (i – 2j - 8k) N, act upon a body of mass 3.0 kg. No other forces act upon the body at this time. What do you know must be true? Newton’s First Law Newton’s Second Law Newton’s Third Law Define Inertia: Sample Problem: A tug-of-war team ties a rope to a tree and pulls hard horizontally to create a tension of 30,000 N in the rope. Suppose the team pulls equally hard when, instead of a tree, the other end of the rope is being pulled by another tug-of-war team such that no movement occurs. What is the tension in the rope in the second case? Mass: Weight: 1 AP Physics – Newton’s Laws – Force and Motion Problem: determine the normal force acting on a 5.0 kg box sitting on a flat table. 1st or 2nd Law Problems 1. Identify the system to be analyzed. This may be only a part of a more complicated system. This is really the most important step. 2. Select a reference frame or coordinate system, stationary or moving, but not accelerating, within which to analyze your system. 3. Identify all forces acting on the system. Ignore the others. This is best done by drawing a Free Body Diagram! 4. Set up F = ma equations for each dimension. Solve for relevant unknowns. 5. Use kinematics or calculus where necessary to calculate more about the motion. Problem: Now determine the normal force acting on a 5.0 kg box sitting on a flat table. Sample Problem: A 5.00-g bullet leaves the muzzle of a rifle with a speed of 320 m/s. The bullet is accelerated by expanding gases while it travels down the 0.820 m long barrel. Assuming constant acceleration and negligible friction, what is the force on the bullet? Problem: Now determine the normal force acting on a this 5.0 kg box sitting on a ramp at angle =30o. Sample Problem: A 3.00 kg mass undergoes an acceleration given by a = (2.50i + 4.10j) m/s2. Find the net force F and its magnitude. Normal force Definition: Always calculate the normal force by considering all forces that have components perpendicular to a surface. 2 AP Physics – Newton’s Laws – Force and Motion Sample problem: derive a formula for acceleration, assuming the table is frictionless. Tension Definition: Why can we depict tension as pulling in opposite directions on two different connected objects? Problem: What is the tension is the cable attached to a 5,000 kg elevator that starts on the ground floor at rest and accelerates upward, reaching a speed of 3.0 m/s in 2 seconds? Sample problem: derive a formula for the tension T in the Sample problem: derive a formula for acceleration, assuming the table is frictionless 3 AP Physics – Newton’s Laws – Force and Motion Atwood machine Definition: Friction Definition: Problem: For the Atwood machine shown, derive an equation which can be used to find g, the gravitational acceleration, from a measured value of What is static friction? What is kinetic friction? Problem: How high up the frictionless ramp will the block slide? Problem: Calculate acceleration of the 5 kg block. Table and pulley are magic and frictionless. Calculate tension in the string. Why is it disadvantageous for cars to skid to a stop? 4 AP Physics – Newton’s Laws – Force and Motion Draw free body diagrams that include friction for a body which is Problem: Assume a coefficient of static friction of 1.0 between tires and road and a coefficient of kinetic friction of 0.80 between tires and road. How far would a car travel down a 15o incline after the driver applies the brakes if it skids to a stop? Assume a speed before brakes are applied is 26 m/s. Sample problem: A 1.00 kg book is held against a wall by pressing it against the wall with a force of 50.00 N. What must be the minimum coefficient of friction between the book and the wall, such that the book does not slide down the wall? Centripetal Force Definition: Examples: Problem: Assume a coefficient of static friction of 1.0 between tires and road. What is the minimum length of time it would take to accelerate a car from 0 to 60 mph? How to begin centripetal force problems: 5 AP Physics – Newton’s Laws – Force and Motion Problem: Find the minimum safe turning radius for a car traveling at 60 mph on a flat roadway, assuming a coefficient of static friction of 0.70. Problem: You swing a 0.25-kg rock in a vertical circle on a 0.80 m long rope at 2.0 Hz. What is the tension in the rope a) at the top and b) at the bottom of your swing? Problem: Derive the expression for the period best banking angle of a roadway given the radius of curvature and the likely speed of the vehicles. Problem: A 40.0 kg child sits in a swing supported by 3.00 m long chains. If the tension in each chain at the lowest point is 350 N, find a) the child’s speed at the lowest point and b) the force exerted by the seat on the child at the lowest point. Non-uniform Circular Motion Characteristics: Problem: A 900-kg automobile is traveling along a hilly road. If it is to remain with its wheels on the road, what is the maximum speed it can have as it tops a hill with a radius of curvature of 20.0 m? 6