Forces AP Physics C What is a Force? Simply put, a force is a push or a pull. The unit for force is the Newton (N). There are forces that require contact: Friction Tension Normal Force

Applied Force There are also forces that do not require contact: Gravity Electric Force Magnetic Force Newtons Laws Isaac Newton developed three laws to govern the motion of macroscopic objects.

These laws relate the forces acting on an object to the motion of the object. Newton first published these laws in his 1687 book Philosophi Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), Newtons First Law Newtons First Law: Unless acted upon by an unbalanced force, and object at rest will stay at rest, and an object in motion will stay in motion at a constant

velocity (that means same speed and direction). The first law is known as the law of inertia. Inertia is Latin for lazy. Mass is how we measure the inertia of an object. The more mass something has, the harder it is to change its motion.

Newtons Second Law Newtons Second Law: The vector sum of all forces acting on an object will equal the product of the objects mass (inertia) and acceleration. There are two very important things to recognize in this formula: Both acceleration and net force are vectors, and they must point in the same direction. It is NET FORCE, which means the vector sum of all the forces acting on an object. Newtons Third Law

Newtons Third Law: For every action, there is an equal and opposite reaction. The third law means that if object A exerts a force on object B, then object B exerts a force of equal magnitude on object A in the opposite direction. This is commonly misunderstood, because we tend to think that objects with more mass exert larger forces than objects with less mass.

What we need to realize is that in a collision between something big and something small, we are seeing the ACCELERATION, NOT THE FORCE. Gravity (Weight) The force of gravity (often called weight), is a non-contact force. Gravity always points down. Mass and weight are not the same

thing, but they are related. More mass means more weight. Not every force will have a formula to directly calculate it, but gravity does. = The force of gravity (weight) is the product of mass and the acceleration due to gravity. Make sure not to confuse the force

of gravity and acceleration of gravity. Normal Force Imagine a book sitting on a table. Gravity pulls down on it, but it does not move. This means there must be another force acting on the book. We call this the normal force. Normal force is the response to some applied force (often gravity). In math and physics, normal means perpendicular. The normal force is always directed perpendicular to the surface. There is not a formula to directly calculate the normal force, it is found using Newtons second law.

Tension If a rope or a wire is pulled on, we call it a tension force. Tension always points along the rope. Like normal force, tension is a resultant force, meaning there is not a specific formula to calculate it. To find tension in a problem, use Newtons second law. Friction Friction, like the normal force, is exerted by a surface. The frictional force is always parallel to the surface.

Kinetic friction acts as an object slides across a surface. Kinetic friction is a force that always opposes the motion. Static friction is the force that keeps an object stuck on a surface and prevents its motion relative to the surface. Static friction points in the direction necessary to prevent motion. Free Body Diagrams When analyzing the forces acting on an object, we start by drawing a free body diagram. From the center of the object, we draw vectors to represent each force acting on the object. It is very important to label each vector with the proper force!

Example A ball, hanging from the ceiling by a string, is pulled back and released. Which is the correct free-body diagram just after its release? Example A car is parked on a hill. Which is the correct free-body diagram? Example A car is towed to the right at constant speed. Which is the correct free-body

diagram? Static Friction The figure shows a person pushing on a box that, due to static friction, isnt moving. Looking at the free-body diagram, the x-component of Newtons first law requires that the static friction force must exactly balance the

pushing force: Static friction points in the direction opposite to the way the object would move if there were no static friction. Static Friction Static friction continues to grow as you push harder and harder.

Eventually static friction reaches a maximum: The letter represents the coefficient of static friction, which is a dimensionless quantity that represents the roughness between objects. It is important to realize that static friction CAN be this maximum

value, but does not have to be that large. Kinetic Friction If an applied force is larger than maximum static friction, the object starts moving. Friction still exists however, and we call this kinetic friction. The formula for kinetic friction

is: The coefficient of kinetic friction will always be less than the coefficient of static friction for two objects. This can apply to an object that is moving at constant velocity or accelerating.

Friction Example A box with a weight of 100 N is at rest. It is then pulled by a 30 N horizontal force. Does the box move? Example A 10-kg box is being pulled across the table to the right at a constant speed with a force of

50N. Calculate the Force of Friction. Calculate the Normal Force. Example A car with a mass of 1500 kg is being towed by a rope held at a 20 angle to the horizontal. A friction force of 320 N opposes the cars motion. What is the tension in the rope if the car goes from rest to 12 m/s in 10 s? Apparent Weight

The weight of an object is the force of gravity on that object. Your sensation of weight is due to contact forces supporting you. This force could either be a normal force or a tension, depending on the situation. The most common example is your apparent weight while standing in an elevator. Sometimes you feel heavy in an elevator,

and sometimes you feel light. That feeling is the normal force that pushes up on you. Apparent Weight If you are moving upwards and speeding up, your acceleration points up. This means the net force on you must also point up, which means that the normal force must be larger than

gravity. This is why you feel heavy! = If your acceleration points down, then it is negative. This would mean that you feel lighter than you are because normal force is smaller than gravity. Example

Brians mass is 70 kg. He is standing on a scale in an elevator that is moving at 5.0 m/s. As the elevator stops, the scale reads 750 N. Before it stopped, was the elevator moving up or down? What is the magnitude of Brians acceleration? How long did the elevator take to come to rest? Inclined Planes A common force problem in physics involves boxes on inclined planes. In these kinds of problems, we have to

break forces into components and use Newtons second law to calculate forces and accelerations that are parallel and perpendicular to the ramp. Example A 46 g domino slides down a 30 degree incline at a constant speed. What is the coefficient of friction? Example

A boy and his sled have a combined mass of 65 kg. What is their acceleration as they start down an icy 22.6 degree incline with a coefficient of friction equal to 0.10? The boy is then pulled back to the top of the hill at a constant speed by a tow rope. What is the tension in the rope? Suspended Objects Another common example in forces is an object being suspended from multiple ropes.

The key to solving these problems is to break forces into horizontal and vertical components and use Newtons second law in both directions. The net force on the object is equal to zero! Example If the suspended mass weighs 50 N,

calculate the tension in the horizontal rope. Systems of Objects If objects are in contact (either pushing against each other or connected with a rope), we can consider them to be a single system. This means that the magnitude acceleration (if there is any) is the

same for all objects in the system. To find the forces between each object in the system, you can apply Newtons second law to the system to find the acceleration. This acceleration can then be used to find each individual force, These forces can also be found using proportional reasoning. Example

The figure to the right shows a 5.0 kg block A being pushed with a 3.0 N force. In front of this block is a 10 kg block B; the two blocks move together. What force does block A exert on block B? Example Boxes A and B are being pulled to the right on a frictionless surface; the boxes are speeding up. Box A has a larger mass than Box B. Which tension force is larger?

Atwood Machines Atwood machines are devices that use pulleys and ropes to raise or lower masses. The keys to solving Atwood problems: The tension in a single rope is the same everywhere (if the rope is massless!). The magnitude of acceleration (if there is any) is the same for all objects in the system. FBD on each object in the system!

Example A 200 kg set used in a play is stored in the loft above the stage. The rope holding the set passes up and over a pulley, then is tied backstage. The director tells a 100 kg stagehand to lower the set. When he unties the rope, the set falls and the unfortunate man is hoisted into the loft. What is the stagehands acceleration?

Example A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable. Air Resistance (Drag) The air exerts a drag force on objects as they move through the air. The drag force direction is opposite the

objects velocity. Factors that commonly increase air resistance include: High velocity. Large surface area. Small mass. Often the drag force will be modeled with either linear or quadratic drag. You will be told in a problem which one to use (linear is more commonly used).

= Terminal Velocity The drag force from the air increases as an object falls and gains speed. If the object falls far enough, it will eventually reach a speed at which the drag force

and gravity are equal. At this speed, the net force is zero, so the object falls at a constant speed, called the terminal speed. Terminal Velocity In a problem with drag, you may have to write out (and possibly solve) a first

order differential equation for the velocity of an object. This is done using Newtons second law as shown below. The solution to this differential equation is a logarithmically growing function that

asymptotically reaches the terminal velocity.