Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 13, 14, 15

Newton’s Laws 1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration 2nd Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. 3rd Law: For every action there is an equal, but opposite reaction

Newton’s law of gravitation

Falling with air resistance

Terminal Velocity with Coffee Filters where is the resistance force. 1.A penny and a quarter dropped from a ladder land at the same time (air resistance is negligible). 2.A coin dropped in a coffee filter from a ladder lands later than a coin without coffee filter (the terminal velocity is smaller for larger cross-section area). 3.A quarter dropped in a coffee filter will land faster than a penny in a coffee filter (the terminal velocity is larger for larger mass) 4.Two identical coins dropped in coffee filters of different diameters land at different times (the terminal velocity is smaller for larger cross-section area).

Resistance force: A – area of the projectile For a spherical projectile in air at STP: Terminal velocity: A 70-kg man with a parachute: v T ~ 5 m/s A 70-kg man without a parachute: v T ~ 70 m/s

Newton’s 1 st Law A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration

Aristotle: a natural state of an object is at rest; a force is necessary to keep an object in motion. It follows from common sense. Galileo: was able to identify a hidden force of friction behind common- sense experiments B.C.

Galileo: If no force is applied to a moving object, it will continue to move with constant speed in a straight line Galilean principle of relativity: Laws of physics (and everything in the Universe) look the same for all observers who move with a constant velocity with respect to each other. Inertial reference frames

Kinetic Friction For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write F Friction =  Kinetic N Here  is a constant Warning: –THIS IS NOT A VECTOR EQUATION!

Static Friction This is more complicated For static friction, the friction force can vary F Friction   Static N Example of the refrigerator: –If I don’t push, what is the static friction force? –What if I push a little?

H Coefficient of friction:  What is the normal force? What is the velocity of the block when it reaches the bottom?

Newton’s 3 rd Law For every action there is an equal, but opposite, reaction

Skater Skater pushes on a wall The wall pushes back –Equal and opposite force The push from the wall is a force –Force provides an acceleration –She flies off with some non-zero speed

P m1m1 m2m2 No friction m1m1 Free body diagram m1m1 m1gm1g P N1N1 F 21 m2gm2g F 12 N2N2 m2m2 F 12 =F 21

Quiz a) A crate of mass m is on the flat bed of a pick up truck. The coefficient of friction between the crate and the truck is . The truck is traveling at the constant velocity of magnitude V 1. Draw the free body diagram for the crate. b) The truck starts to accelerate with an acceleration a c. Draw the free body diagram for the crate, if the crate does not slip.

A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is If the larger block is on a frictionless table, what is the largest horizontal force that can be applied to it without the small block slipping?

A block of mass 20 kg is pushed against a vertical surface as shown. The coefficient of friction between the surface and the block is 0.2. If θ=30 0, what is the minimum magnitude of P to hold the block still? θ P

V0V0 A block of mass m is given an initial velocity V 0 up an inclined plane with angle of incline θ. Find acceleration of the block if a)  = 0 b) non-zero 

A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge. What must the magnitude of F be if the block is to remain at a constant height above the tabletop?

A Problem With First Year Physics Strings and Pulleys m1m1 m 1, m 2 are given m 2 >m 1 m2m2 String is massless and unstretchable Find accelerations of m 1 and m 2 (assume no friction in pulley)

Block 1, of mass m 1, is placed at rest on an inclined plane. It is attached by a massless, unstretchable string to block 2, of mass m 2. The pulley is massless and frictionless and just changes the direction of the tension in the string. The coefficient of friction between the plane and m 1 is the constant . 2 1 Determine what range of values for mass m 2 will keep the system at rest. Find acceleration if mass 2 goes down.

F Find F necessary to drag the box 1 at constant speed. 1 2 Friction everywhere.

The advantage of a pulley What minimum force F is needed to lift the piano of mass M?

The Elevator Problem

Have a great day! Reading: Chapter 7 Hw: Chapter 6 problems and exercises