Warm Up The coefficient of friction is 0.17, and the object is accelerating at 3m/s2 to the right, what is the force in each direction and what is the net force & direction? 50kg

What is the car doing? Is it moving and in what direction? Warm Up What is the car doing? Is it moving and in what direction?

Newton’s Second Law

But first… Review: Newton’s First Law If an object experiences NO net force…. Resting objects remain at rest. Moving objects move at a constant velocity.

Newton’s First Law Also known as the Law of Inertia Inertia: An object’s tendency to keep on doing what it’s already doing.

Newton’s First Law Inertia: An object’s tendency to keep on doing what it’s already doing. An object at rest will remain at rest…

Law of Inertia: An object in motion will continue in motion…

Inertia Inertia is a term used to measure the ability of an object to resist a change in its state of motion. An object with a lot of inertia takes a lot of force to start or stop; an object with a small amount of inertia requires a small amount of force to start or stop. The word “inertia” comes from the Latin word inertus, which can be translated to mean “lazy.”

Inertia Inertia is a term used to measure the ability of an object to resist a change in its state of motion. Mass is a measure of inertia. The higher the mass of an object is, the more it resists changes to its motion:

Law of inertia: (click here) The law of inertia and YOU!

Equilibrium The condition of zero acceleration is called equilibrium. In equilibrium, all forces cancel out leaving zero net force. Objects that are standing still are in equilibrium because their acceleration is zero. Objects that are moving at constant speed and direction are also in equilibrium. A static problem usually means there is no motion.

Calculate force A woman is holding two dogs on a leash. If each dog pulls with a force of 80 newtons, how much force does the woman have to exert to keep the dogs from moving? 1) You are asked for force (F). 2) You are given two 80 N forces and the fact that the dogs are not moving (a = 0). 3) Newton’s second law says the net force must be zero if the acceleration is zero. 4) The woman must exert a force equal and opposite to the sum of the forces from the two dogs. Two times 80 N is 160 N, so the woman must hold the leash with an equal and opposite force of 160 N.

Newton’s Second Law The acceleration of an object is: Directly proportional to the net force acting on it, and… Inversely proportional to its mass

What does that mean? The acceleration of an object is: Directly proportional to the net external force acting on it (The stronger the force applied to an object, the greater the acceleration will be.) Inversely proportional to its mass (The heavier the object, the less it will accelerate for a given force.)

Newton's Second Law If you apply more force to an object, it accelerates at a higher rate.

Newton's Second Law If an object has more mass, it accelerates at a lower rate because it has more inertia.

Practice: Calculating acceleration A cart rolls down a ramp. The cart has a mass of 500 grams (0.5 kg). Using a spring scale, you measure a net force of 2 newtons pulling the car down. Calculate the acceleration of the cart. 1) You are asked for acceleration (a). 2) You are given mass (m) and force (F). 3) Newton’s second law applies. a = F/m 4) Plug in numbers. Remember that 1 N = 1 kg·m/sec2. a = (2 N) / (0.5 kg) = (2 kg·m/sec2) / (0.5 kg) = 4 m/sec2

Calculating acceleration Three people are pulling on a wagon applying forces of 100 N,150 N, and 200 N. The wagon has a mass of 25 kilograms. Determine the acceleration and the direction the wagon moves. 1) You are asked for the acceleration (a) and direction. 2) You are given the forces (F) and mass (m). 3) The second law relates acceleration to force and mass (a = F ÷ m). 4) First, assign positive and negative directions. Next, calculate net force. Finally, use the second law to determine the acceleration from the net force and the mass. 5) F = -100N - 150 N + 200N = -50N a = (-50 N)÷(25 kg) = -2 m/sec2. The wagon accelerates 2 m/sec2 to the left.

Calculating force An airplane needs to accelerate at 5 m/sec2 to reach take-off speed before reaching the end of the runway. The mass of the airplane is 5,000 kilograms. How much force is needed from the engine? 1) You asked for the force (F). 2)You are given the mass (m) and acceleration (a). 3) The second law applies. F = ma 4) Plug in numbers. Remember that 1 N = 1 kg.m/sec2. F = (5,000 kg) x (5 m/sec2) = 25,000 N

More on weight…. Weight (as you know) is a force. Weight is the force exerted on an object by gravity. The magnitude of weight is found by Newton’s Second Law: F = m x a Weight = mass x (9.8 m/s2)

Friction the force exerted by a surface that opposes the motion of an object moving (or trying to move) across it

Static Friction The force that prevents an object from moving when you push it. “static” means “not moving”

Static Friction Imagine that you are trying to push a box across the floor. If you apply a very small force, the box will not move. This must mean that the frictional force is equal to the force with which you are pushing the box. (Why?)

Static Friction If you push the box a bit harder, it might still remain stationary. The frictional force must therefore have increased, or the box would have moved. As long as the box doesn’t move, the force of static friction is always equal to and opposite in direction to the applied force.

Static Friction If you continue to push harder, eventually a point is reached when the frictional force increases no more. If you push ever so slightly harder, the box will start to move.

Static Friction Static frictional forces are caused by the interlocking of the irregularities of two surfaces. Even surfaces that seem quite smooth are not really smooth!

Static Friction The static friction force between two objects is not constant, but increases until it reaches a maximum value. When the frictional force is at its maximum, the body in question will be on the verge of moving. Animation

Kinetic Friction the force that opposes motion of an object moving across a surface. will be less than the maximum static friction. (It’s harder to get a heavy object to start moving than it is to keep it moving.)

Friction The force of friction is proportional to the normal force. It is easier to push a chair across the floor at a constant speed than to push a heavy desk across the floor at the same speed.

The coefficient of friction (Here comes the math!)

Coefficient of Friction The coefficient of friction is a number which represents the friction between two surfaces. The symbol usually used for the coefficient of friction is µ.

The coefficient of friction depends on the type of surface: Imagine sliding across a sheet of ice, and then trying to slide over a sheet of sandpaper. The sandpaper exerts more frictional resistance.

Coefficient of friction Has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher values.

Coefficient of Friction The frictional force is equal to the coefficient of friction × the normal force. Ff = µFN Where µ is the coefficient of friction, and FN is the normal force.

Practice problem Ff = µFN A wooden pallet carrying a load of 600 kg rests on a wooden floor. A forklift driver decides to push it without lifting it. What force must be applied to just get the pallet moving? (µs = 0.28) Ff = µFN

Practice problem A 24 kg crate initially at rest on the floor requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor. Ff = µFN