Forces Chapter 6.1

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.

Acceleration What may cause an object to experience a change in velocity? –Force Forces are often described as a push or pull. A force may cause an object to speed up. –Acceleration (positive) A force may cause an object to slow down. –Acceleration (negative) or deceleration A force may also cause an object to change direction.

Acceleration Force Force is a vector –It has magnitude –It has direction A force may also cause an object to change direction. –This may or may not include a change in magnitude

Types of Forces Gravitational Electromagnetic Normal Frictional Tension

Force Force is a vector quantity, therefore it has both magnitude and direction.

Force In the English system, we start with pounds and derive a unit of mass (the slug) – 1 pound accelerates 1 slug at a rate of 1ft/sec 2 In the metric system we start with mass – what is the force that accelerates 1 kg at a rate of 1m/sec 2 ?

Force The SI unit for force is the Newton. –1 Newton is the amount of force required to accelerate a 1 kg mass 1 m/s 2. –The Newton is a derived unit where: 1N = 1kgm/s 2 Kg, m, second are fundamental units

Force 1 Newton is the amount of force required to accelerate a 1 kg mass 1 m/s 2. –So 1N causes a mass to change its velocity at a rate of 1m/sec. –Example: A 1kg object is accelerated by a 1N force. If it starts with V i = 0, what is V f after one second? Two? Four? Hint: a = 1m/sec 2

The System and Environment The object of interest is called the System. The area around the object is called the Environment. FgFg FNFN System Environment

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 forces act over distances without a need for direct contact. Electromagnetic forces and gravity are long-range forces.

Free Body Diagram FgFg FNFN = F N = Force of Desk on Book F g = 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. System

Free Body Diagrams FgFg FNFN = F w = Force of hanging mass on Book F g = Force of Gravity on Book Is the book accelerating? System 5 kg F N = Force of Desk on Book

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

Newton’s 2 nd Law and Force vs. Acceleration How does acceleration relate to force? –As the force on an object increases, the rate of acceleration will increase. Acceleration m1m1 m2m2 m 2 > m 1 Note: The slope of the line in a F vs. a graph will equal the mass of the object. The greater the slope, the greater the mass

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

Newton’s 2 nd Law Force Constant / Increasing Mass If the applied force to a system is held constant and the mass is increased from m 1 to m 2, what would a velocity vs. time graph look like? Time m1m1 m2m2 As the mass increases, the rate of acceleration will decrease. m 2 > m 1

Newton’s 2 nd Law Mass Constant / Increasing Force If the mass is held constant and the force applied to a system is increased from F 1 to F 2, what would a velocity vs. time graph look like? Time F2F2 F1F1 As the force increases, the rate of acceleration will increase. F 2 > F 1

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?

Diagram the problem F net = F person 1 + F person 2 – F opposing force

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) = ?

Perform Calculations F net = F person 1 + F person 2 - F opposing Where: oF net = ma Substitute for F net and solve for a: oma = F person 1 + F person 2 - F opposing oa = (F person 1 + F person 2 - F opposing )/m oa = (275 N N – 560 N)/1850 kg oa = m/s 2 o If there was no opposing force, how would the rate of acceleration change? o What do you think is the source of the opposing force? It would increase. Friction.

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 2 nd Law of Motion states that the rate of acceleration of an object is proportion 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.