PHYS16 – Lecture 10 & 11 Force and Newton’s Laws September 29 and October 1,

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.

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

Mechanical Equilibrium Mechanical Equilibrium – when F NET =0 – Static Equilibrium v= 0 F NET =0 Example – book on a table – Dynamic Equilibrium v= constant F NET =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

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 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? – |F f |= 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)