Force & Newton’s Laws of Motion

FORCE Act of pulling or pushing Act of pulling or pushing Vector quantity that causes an acceleration when unbalanced Vector quantity that causes an acceleration when unbalanced Forces can cause objects to… Forces can cause objects to… Start movingStart moving Stop movingStop moving And/or change directionAnd/or change direction

NEWTON * SI Unit for Mass = kilogram (kg) * SI Unit for Acceleration = meters/second 2 * SI Unit for Force = Newton (N) * Newton: Amount of force that, when acting on a 1 kg mass, produces an acceleration of 1 m/s 2 * 1 N = 1 kg x 1 m/s 2

NEWTON’S FIRST LAW  Objects move at constant velocity unless acted upon by a net force ** Every object continues in a state of rest, or of motion in a straight line at constant speed, unless it is compelled to change that state by forces exerted upon it

MASS  Measures an object’s resistance to change velocity  Quantity of matter in an object  Mass is NOT weight

Gravitational Force: WEIGHT  Force of gravity on an object  Downward pointing vector  W = mg Weight = mass x acceleration due to Weight = mass x acceleration due to gravity gravity

QUESTION * What is Frank’s weight on Earth? (HINT: His mass = 80.0 kg) Answer: W = mg W = (80 kg)(9.8 m/s 2 ) W = 784 N

NET FORCE * In the absence of force… - Objects at rest, remain at rest - Objects in motion, continue in motion * NET FORCE: - Combination of all forces acting on an object - Net force  Changes an object’s state of motion

NET FORCE *Remember  Force = Vector, represented by an arrow Applied ForcesNet Forces 5 N 10 N 15 N 10 N5 N 0 N

An object is in equilibrium when it has zero acceleration Net force on the object equals zero EQUILIBRIUM 5 N

NEWTON’S SECOND LAW  Acceleration of an object Directly proportional to the net force acting on the object Directly proportional to the net force acting on the object Inversely proportional to the object’s mass Inversely proportional to the object’s mass Net force = mass x acceleration Net force = mass x acceleration (Newtons)= (kg) x (m/s 2 ) Rearranged:

Question  What is the box’s acceleration? Mass of the box = 15 kg Mass of the box = 15 kg F = 158 N F = 158 N a = ? a = ?

Question  What is the box’s acceleration? Answer: ΣF = ma F + (−mg) = ma a = (F − mg)/m a = (158 N −147 N)/(15 kg) a = 0.73 m/s 2 (upward)

NEWTON’S THIRD LAW Forces come in action-reaction pairs Forces come in action-reaction pairs Equal in strength, opposite in directionEqual in strength, opposite in direction Forces act on different objectsForces act on different objects F ab = −F ba F ab = −F ba Force of a on b = opposite of force of b on a Force of a on b = opposite of force of b on a

Question  The weight of the apple is 1.5 N. When the apple hits the ground, what force does it exert on the Earth? Answer: 1.5 N upward Answer: 1.5 N upward

Equilibrium: When the Net Force Equals Zero What forces act on a motionless block sitting on a table? What forces act on a motionless block sitting on a table?

NORMAL FORCE (F N ) Occurs when 2 objects are in direct contact Occurs when 2 objects are in direct contact Acts at right angles to the surface Acts at right angles to the surface Perpendicular to the surface Perpendicular to the surface

TENSION (F T )  Force conveyed through a string, chain, rope, tendon, etc.

A massless rope will transmit tension undiminished from one end to the other. If the rope passes around a massless, frictionless pulley, the tension will be transmitted to the other end of the rope undiminished.

Free-body Diagrams  Shows all external forces acting on a body Force vectors Force vectors Point in the direction of the forcePoint in the direction of the force Often drawn from the originOften drawn from the origin

Net force on the car: 275 N N – 560 N = +110 N Directed along the + x axis of the coordinate system.

If the mass of the car is 1850 kg then, by Newton’s second law, the acceleration is

FRICTION Resistive force Resistive force Acts in a direction opposite to the direction of the relative motion of 2 contacting surfaces Acts in a direction opposite to the direction of the relative motion of 2 contacting surfaces Varies by materials in contactVaries by materials in contact Proportional to the normal force between the objectsProportional to the normal force between the objects Draw vector parallel to the surface Draw vector parallel to the surface

Note that the magnitude of the frictional force does not depend on the contact area of the surfaces.

The Force of FRICTION  Static Friction: Force that resists the initiation of sliding motion between 2 surfaces that are in contact and at rest Force that resists the initiation of sliding motion between 2 surfaces that are in contact and at rest f s, max =  s F N f s, max =  s F N f s, max = Maximum static friction forcef s, max = Maximum static friction force  s = Coefficient of static friction F N = Normal forceF N = Normal force

When the two surfaces are not sliding across one another the friction is called static friction.

The Force of FRICTION  Kinetic Friction: The force that opposes the movement of 2 surfaces that are in contact and are sliding over each other The force that opposes the movement of 2 surfaces that are in contact and are sliding over each other f k =  k F N f k =  k F N f k = Force of Kinetic Frictionf k = Force of Kinetic Friction  k = Coefficient of Kinetic Friction F N = Normal ForceF N = Normal Force

The sled comes to a halt because the kinetic frictional force opposes its motion and causes the sled to slow down. Suppose the coefficient of kinetic friction is 0.05 and the total mass is 40kg. What is the kinetic frictional force?

Suppose the coefficient of kinetic friction is 0.05 and the total mass is 40kg. What is the kinetic frictional force? N = mg = (40kg)(9.8m/s 2 ) = 392 N f k = (0.05)(392N) = 19.6N

The direction of force and acceleration vectors can be taken into account by using x and y components. is equivalent to

4.11 Equilibrium Application of Newton’s Laws of Motion Definition of Equilibrium An object is in equilibrium when it has zero acceleration.