Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 10,11

Falling with air resistance

Terminal Velocity with Coffee Filters where is the resistance force. A penny and a quarter dropped from a ladder land at the same time (air resistance is negligible). 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). 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) 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: Terminal velocity: A – area of the projectile For a spherical projectile in air at STP: Terminal velocity: A 70-kg man with a parachute: vT ~ 5 m/s A 70-kg man without a parachute: vT ~ 70 m/s

Dynamics Connection between force and motion The concept of force gives us a quantitative description of the interaction between two bodies or between a body and its environment

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

Newton’s 1st 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. 384-322 B.C. Galileo: was able to identify a hidden force of friction behind common-sense experiments 1564-1642

Galileo: If no force is applied to a moving object, it will continue to move with constant speed in a straight line Inertial reference frames 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.

2nd Law From experiments we know: Force is a vector The direction of acceleration vector is the same as the direction of the force vector The magnitude of the force and acceleration are related by a constant which depends on number of blocks involved.

Newton’s second law The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

-is deviation from the natural length Gravitational force Normal force Force exerted by a spring: Hooke’s law: If spring is stretched or compressed by some small amount it exerted a force which is linearly proportional to the amount of stretching or compressing. The constant of proportionality is called the spring constant -is deviation from the natural length

The force resisting the pull of the spring – friction There is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates. The maximum of the force of friction varied linearly with the amount that the block pushes on the table.  - coefficient of friction, is the vertical force exerted by the block on the table The friction force only exists when there is another force trying to move an object

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

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

A Recipe for Solving Problems Sketch Isolate the body (only external forces but not forces that one part of the object exert on another part) 2. Write down 2nd Newton’s law Choose a coordinate system Write 2nd Newton’s law in component form: 3. Solve for acceleration

Pulling Against Friction A box of mass m is on a surface with coefficient of kinetic friction m. You pull with constant force FP at angle Q. The box does not leave the surface and moves to the right. What is the magnitude of the acceleration? What angle maximizes the acceleration? Q

Is it better to push or pull a sled? You can pull or push a sled with the same force magnitude, FP, and angle Q, as shown in the figures. Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, m, which is better? FP FP

Coefficient of friction:  H θ 1) Find the force of friction if the block is at rest. 2) The block slides down the incline. What is the velocity of the block when it reaches the bottom?

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 V1. Draw the free body diagram for the crate. b) The truck starts to accelerate with an acceleration ac. Draw the free body diagram for the crate, if the crate does not slip.

Have a great day! Reading: Chapter 5,6 Hw: Chapter 6 problems and exercises