AP Physics I.B Newton’s Laws of Motion

B.1 An interaction between two bodies resulting in a push or a pull is a force. Forces are of two types: contact and field forces

Newton’s First Law – an object at rest will remain at rest, or an object in motion at a constant velocity will continue at a constant velocity, unless acted upon by a net force.

The tendency of objects to resist changes in their state of motion is called inertia. The First Law is often called the Law of Inertia. Why?

An unlikely trio – Mr. Evans, James Lovell and Sir Isaac Newton

Net force – the sum of all the forces acting on an object

If the net force is zero... The object is not moving or... The object is moving at a constant velocity therefore... The object is in equilibrium

B.2 Newton’s Second Law

The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.

Net force is a vector in the same direction as the acceleration

Note! If an object accelerates then the net force is NOT zero. If the net force is zero, then the object is moving with a constant velocity or it is at rest.

Use free body diagrams to show all of the forces acting on an object. Drawing the correct FBD is half the battle.

Practice FBD’s Crate at rest on the floor. Mad dad kicks crate with foot across frictionless floor. Crate slides with constant velocity across frictionless floor. Crate slides across rough area. Crate slides up a ramp with friction. Crate slides down a ramp with friction.

Ex. Huey pulls on the front legs of a 4.0 kg cat with a force of 8.0 N to the right. Dewey, pulls on the back legs of a cat with a force of 20.0 N to the left. What is the acceleration of the cat assuming the legs remain attached?

Newton’s Third Law (highly misunderstood)

Newton’s Third Law – when one object exerts a force on a second object, the second object exerts a force that is equal in magnitude, but in the opposite direction to that of the first

“This third law is confusing!” Remember – Newton’s Third Law deals with two forces and two objects, not two forces on one object.

Problem solving strategies Draw a free body diagram. Is the object in equilibrium (at rest or constant velocity)or is it accelerating? If in equilibrium: the sum of the upward forces = the sum of the downward forces and the sum of the forces to the right = the sum of the forces to the left. If accelerating: write an expression for the net force and use the Second Law.

Mass and weight

Ex. What is the mass of a watermelon that has weight of 60.0 N?

The Normal Force “As opposed to the abnormal force” The force a surface exerts on an object, perpendicular to the surface

Some instructive illustrations

Ex. A book with a mass of 2.0 kg rests on a table. What is the normal force on the book by the table?

The normal force and weight on an inclined plane

Apparent weight (how much your mother or father weighs)

Setting up the elevator problem.

Ex. A crate slides across a rough floor with an initial speed of 2.5 m/s. The coefficient of friction between the floor and crate is What is the distance required for the crate to come to rest?

Ex. A crate with a mass of 20.0 kg is pulled across a wooden floor with a force of 90.0 N. The coefficient of kinetic friction between the crate and the floor is What is the acceleration of the crate?

Tension “These forces are killing me, give me an Excedrin.”

Tension is the force a rope, string, chain, cable, sinewy cat gut, etc. exerts on an objects. All of these forces can pull only, and not push. Therefore, the direction of tension is always away from the object.

Ex. A can of paint with a mass of 6.0 kg hangs from a rope. If the can is pulled to a rooftop with a constant velocity of 1.0 m/s, what is the tension in the rope?

Ex. What is the tension in a rope that lifts a 50.0 N object with an acceleration of 10.0 m/s 2 ?

AP Type Problems

Pulleys and hanging blocks. If you are not concerned with tension in the connecting string, treat the blocks as a single system. If you need to find tension, you must consider the blocks separately.

m M Ex. Find the acceleration of the blocks if they are released from rest and m rests on a frictionless surface. What is the tension between the blocks?

6m6m 3m3m m Ex. What is the acceleration of the block with mass 3m? What is the tension in the string above m?

M FTFT FTFT Ex. What is the F T if each string is at an angle θ with the vertical? θθ

75 kg 50º 25º F T1 F T2 Ex. Find F T1 and F T2.

m Ex. A block of mass m slides down a frictionless inclined plane that makes an angle θ with the horizontal. Find the acceleration of the block in terms of the given variables and fundamental constants. θ

m Ex. A block slides down an inclined plane that makes an angle θ with the horizontal. Find the acceleration of the block if the coefficient of kinetic friction between the block and plane is μ. θ