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Forces and Newton's 2nd Law: Understanding Velocity and Acceleration

Learn about the concept of force, different types of forces, free body diagrams, and the relationship between force, acceleration, and velocity according to Newton's 2nd Law.

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Forces and Newton's 2nd Law: Understanding Velocity and Acceleration

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  1. Forces Chapter 6.1

  2. What You Already Learned • Velocity is the ratio of the change in position of an object over a period of time. • Acceleration describes a change in velocity of an object.

  3. Acceleration • What may cause an object to experience a change in velocity? • Force • A force is a push or pull. • A force may cause an object to speed up. • A force may cause an object to slow down. • A force may also cause an object to change direction.

  4. Types of Forces • Gravitational • Electromagnetic • Normal • Frictional • Tension

  5. Force • Force is a vector quantity, therefore it has both magnitude and direction. • The SI unit for force is the Newton. • The Newton is a derived unit where: 1N = 1kg•m/s2 • 1 Newton is the amount of force required to accelerate a 1 kg mass 1 m/s2. • 1 Newton is about the weight of a medium sized apple.

  6. Contact vs. Long Range • Some forces act over distances while others act only when two objects are in contact with one another. • Contact forces exist when two objects are in contact with one another. • Long-range (FIELD) forces act over distances without a need for direct contact. Electromagnetic forces and gravity are long-range forces.

  7. FN System Environment Fg The System and Environment • The object of interest is called the System. • The area around the object is called the Environment.

  8. System FN Fg Free Body Diagram FN = Force of Desk on Book = Fg = Force of Gravity on Book Free-Body diagrams provide a means by which all the external forces acting on a system can be summarized and accounted for, and the resultant vectors determined.

  9. Newton’s 2nd Law • Newton determined that the acceleration of an object is directly proportional to the net unbalanced external force applied to move it and inversely proportional to the mass of the object. Where F = Force in Newtons m = mass of the object a = acceleration of the object

  10. Acceleration Force Newton’s 2nd Law: The relationship between force and acceleration • What will happen to an object’s acceleration if you increase the net force acting on it? • As the force on an object increases, the rate of acceleration will increase. • i.e. Bigger Force = Bigger Acceleration What does the slope of the line in an a vs. F graph equate to?

  11. Force Acceleration Newton’s 2nd Law: The relationship between force and acceleration • How does the graph change if you plot force vs. acceleration instead? • The slope now equals the mass. • Which object on the graph below has a greater mass and how do you know? Since the slope of the line in a F vs. a graph equals the mass, the greater the slope, the greater the mass m2 m2 > m1 m1

  12. Velocity Time Newton’s 2nd Law and velocity vs. time (constant force) • Newton’s 2nd Law indicates that a constant force applied to an object will cause the speed to change at a constant rate. • i.e. Acceleration is constant Note: Remember from kinematics that the slope of the line is equal to a.

  13. m1 Velocity m2 Time Newton’s 2nd LawForce Constant / Different Mass • If the applied force to a system is held constant and the mass is increased from m1 to m2, what would a velocity vs. time graph look like? Force is Constant m2 > m1 More Mass = Less Acceleration.

  14. F2 Velocity F1 Time Newton’s 2nd LawMass Constant / Different Force • If the mass is held constant and the force applied to a system is increased from F1 to F2, what would a velocity vs. time graph look like? Mass is Constant F2 > F1 More Force = More Acceleration.

  15. Example: What is the rate of acceleration? • Two people are pushing a stalled car. The mass of the car is 1850 kg. One person applies a 275 N force while the other applies a 395 N force. A third force of 560 N acts in in the opposite direction compared to the two people. What is the acceleration of the car?

  16. Diagram the problem Fnet = Fperson 1 + Fperson 2– Fopposing force

  17. State the Known and Unknowns • What is known? • Mass (m) = 1850 kg • Force of person #1 (N) = 275 N • Force of person#2 (N) = 395 N • Opposing Force (N) = 560 N • What is not known? • Acceleration (a) = ?

  18. Perform Calculations • Fnet = Fperson 1 + Fperson 2 - Fopposing Where: • Fnet = ma • Substitute for Fnet and solve for a: • ma = Fperson 1 + Fperson 2 - Fopposing • a = (Fperson 1 + Fperson 2 - Fopposing)/m • a = (275 N + 395 N – 560 N)/1850 kg • a = 0.059 m/s2 • If there was no opposing force, how would the rate of acceleration change? • What do you think is the source of the opposing force? It would increase. Friction.

  19. Key Ideas • Force is a vector quantity that is a measure of the magnitude of a push or pull in Newtons. • Forces exist as contact or long range. • Use free body diagrams to represent forces when problem solving. • Newton’s 2nd Law of Motion states that the rate of acceleration of an object is proportional to the force applied and inversely proportional to its mass. • A constant force applied to an object will cause it to accelerate at a uniform rate. • As force increases, acceleration increases. • As mass increases, acceleration decreases.

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