Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 5,6,7

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?

V0 A block of mass m is given an initial velocity V0 up an inclined plane with angle of incline θ. Find acceleration of the block if a)  = 0 b) non-zero 

H βt Coefficient of friction:  V0=0 Find the equation that could be solved to find the velocity of the block when it reaches the top.

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.

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

Skater Equal and opposite force Force provides an acceleration 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 m1 m1 m2 Free body diagram N2 N1 F12 P F21 m2 m1 m2g m1g F12=F21 No friction P m1 m1 m2 Free body diagram N2 N1 F12 P F21 m2 m1 m2g m1g F12=F21

A small block, mass 2kg, rests on top of a larger block, mass 20 kg A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is 0.25. A horizontal force F = 10 N is applied to a larger block. If the larger block is on a frictionless table, find the acceleration of m2 if the blocks move together without slipping.

A small block, mass 2kg, rests on top of a larger block, mass 20 kg A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is 0.25. 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 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=300, what is the minimum magnitude of P to hold the block still? P θ

A wedge with mass M rests on a frictionless horizontal tabletop 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 m1, m2 are given m2>m1 m2 String is massless and unstretchable Find accelerations of m1 and m2 (assume no friction in pulley)

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