PHYS16 – Lecture 10 & 11

Force and Newton’s Laws September 29 and October 1, 2010

http://fashionablygeek.com/wp-content/uploads/2009/09/mass-times-acceleration.gif

Key Concepts: Force

• Force– Definition and Types– Center of Mass– Free Body Diagrams

• Newton’s Laws• Friction

Newton’s Laws – First Law

• A body at rest remains at rest & a body in motion stays in motion unless acted on by a force– Doesn’t seem true because most objects don’t

infinitely stay in motion, why? (friction)– Can see this is true if decrease air friction• Example – Brick pushed along ground vs. Brick in cart

pushed along ground

Newton’s Laws – Second Law

• If there is a NET force then the object is accelerated in the direction of the force.

• The magnitude of the acceleration is proportional to the force and inversely proportional to the object’s mass.

amFNET

What happens if there is no net force?

• Scenario #1 – there are forces acting on the object, but they cancel

• Scenario #2 – there are no forces acting on the object

• If there is no NET force then no acceleration

0NETF

Mechanical Equilibrium

• Mechanical Equilibrium – when FNET=0– Static Equilibrium• v= 0• FNET=0• Example – book on a table

– Dynamic Equilibrium• v= constant• FNET=0• Example – car moving at constant speed

Newton’s Laws – Third Law

• Every action has an equal and opposite reaction

• Does this seem true? If I push a block does it push back on me?– Yes, I just have friction from floor keeping me in place– Can feel pressure of block on fingers

• So all reactionary forces – Normal, Friction, Tension will vary with the amount of applied force

reactionaction FF

Problem #1

• I hold a 0.5 kg mass by a string so that it is still in space. What is the force I apply?– 5 N, upward

Problem #2

• A mass is connected to a string which goes around a pulley. I hold the string at the other end. The mass is 0.5 kg. How much force do I have to apply?– 5 N, downward

Problem #3

• Panda is in a box with a rope at one end. I pull Panda and box at 8.0 N at a constant velocity. The surface has a kinetic friction coefficient of 0.37. What is the mass of Panda and box?– 2.2 kg (there was a brick in the box)– What if I just pull Panda and box without brick at a

constant velocity using a 2 N force, how much is the Panda/box mass? (0.55 kg)

Problem #4

• I have a block with mass m sitting on an incline of θ. Assuming that there is friction, what is the frictional force in terms of m, g, and θ?– |Ff |= mg sin(θ), direction is up the incline parallel

to incline surface

Problem #5

• A cart of mass M sits on a frictionless table. There is a a massless rope connected at one end of the cart that is horizontal, parallel to the table. The rope goes around a massless pulley and then is connected to a hanger of mass m hanging vertically from the pulley. The cart and hanger are accelerated at a value given by a. What is a in terms of M, m, and g?– a=mg/(m+M)