Sec 4-1 Notes Changes in Motion

force – the cause of an acceleration

- the change in an object’s velocity

- SI unit is the Newton (N)

1 N = 1 kgm/s²

Types of forces

contact force – force that arises from the physical contact of two objects

field force – force that can exist between objects, even in the absence of physical contact between the objects

*very important to the study of particle physics

examples: gravity, electric charges, magnetic charges

field theory – the presence of an object effects the space around it so that a force is exerted on any other object within that space

Force diagram – a diagram of the objects involved in a situation and the forces exerted on the objects

- includes all objects and all forces

- treat all objects as point objects and draw the forces from the center

free-body diagram (FBD) – shows only the object and the forces acting on it

- does not show forces exerted by the object

Steps to drawing FBD’s

1. Draw a simple diagram of the object; position the object with an orientation described in the problem.

2. Draw and label vector arrows representing all external forces.

example: a car is being towed. The tow truck exerts a force of 5800N. Gravity exerts a force of 14,700N. The road exerts a force of 13,690N on the car. The friction between the tires and the road exert a backward force of 775N.

Sec 4-2 Notes Newton’s First Law

Galileo – in the 1630s – experimented and hypothesized that it is an objects nature to maintain its motion

1687 – Sir Isaac Newton – formalized this idea

Newton’s First Law

An object at rest remains at rest and an object in motion remains in motion at constant velocity unless the object experiences a net external force.

inertia – the tendency of an object to maintain its state of motion

- its “laziness”

Net external force – the total force resulting from a combination of external forces on an object

- the vector sum of all the forces acting on an object

- also called the Resultant force

Steps to find the Net external force

· Define the problem and identify the variables.

· Select a coordinate system and apply it to the FBD.

· Find the x and y components of all vectors.

· Find the sum of the x forces (SF_x) and the sum of the y forces (SF_y).

· Find the net force (F_net). (Also called the resultant force)

· Evaluate the answer.

example: Derek leaves his physics book on top of a drafting table that is inclined at a 35° angle. The FBD shows the forces acting on the book. Find the net external force acting on the book and determine whether the book will remain at rest in this position.

Mass is a measurement of inertia.

- Imagine applying the same force to a basketball initially at rest and a golf ball initially at rest. How will their accelerations compare?

Objects in motion tend to stay in motion.

***This is such a huge idea!!!***

- seat belts

- unbelted rear-seat passengers

- loose objects in the cargo area

equilibrium – the state in which there is no change in a body’s motion

- an object can be in equilibrium even with many forces acting on it

-the net external force must be equal to zero

equilibrant – the force required to achieve equilibrium

Sec 4-3 Notes Newton’s 2^nd and 3^rd Laws

Newton’s 2^nd Law

The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the objects mass.

SF = ma

Net external force = mass x acceleration

example: A 7.5 kg bowling ball initially at rest is dropped from the top of an 11m building. It hits the ground 1.5s later. Find the net external force on the falling ball.

To solve NSL problems it is sometimes easier to break it into components.

SF_x = ma_x SF_y=ma_y

If the net external force is zero the a = 0, which means the object is experiencing constant velocity or zero velocity.

Concept check:

1. The force of gravity is twice as great on a 2kg rock as it is on a 1kg rock. Which rock accelerates faster?

2. A truck loaded with sand accelerates at .5m/s² on the highway. If the driving force remains the same, what happens to the trucks acceleration if sand leaks at a constant rate from a hole in the truck bed?

Newton’s 3^rd Law

For every action, there is an equal and opposite reaction.

action-reaction pair – a pair of simultaneous equal but opposite forces resulting from the interaction of two objects

- the reaction occurs at the same time as the action

- each force (action/reaction) acts on a different object

example: hammering a nail

action: F_{hammer-on-nail} reaction: F_{nail-on-hammer}

Concept check:

1. A person kicks a football. Believing to know Newton’s 3^rd Law, they claim the football won’t move because your foot exerts a force on the ball and the ball exerts an equal but opposite force on your foot. Therefore F_net = 0, and the ball won’t move.

Sec 4-4 notes Everyday forces

1. weight – the magnitude of the force of gravity acting on an object

W= mg

-we also call it F_g, the force due to gravity

2. Normal force – a force exerted by one object on another in a direction perpendicular to the surface of contact

- We use F_N for the Normal force.

Two situations frequently encountered:

1. No angle – an object is on a level plane.

F_N = -W

2. An angle – an object is on an inclined plane.

1. Define an axis.

2. Draw the FBD for the object.

3. Draw the components of W (or F_g).

4. Use NSL to set up equations in the x and y directions, being careful with +, - signs.

SF_x = ma_x SF_y = ma_y

3. Frictional forces (F_f)

- there are two kinds of frictional forces

static and kinetic

Static friction (F_s) – the resistive force that opposes the relative motion of two contacting surfaces that are at rest with respect to one another

F_s = -F_applied

- as long as the object doesn’t move

- F_s has a maximum value

Kinetic friction (F_k) - the resistive force that opposes the relative motion of two contacting surfaces that are moving past one another

- depends on the surfaces in contact

coefficient of friction (m) – the ratio of the force of friction to the normal force acting between the objects

m_k = F_k / F_N m_s = F_s,max / F_N

or if you rearrange these expressions

F_k = m_kF_N F_s,max = m_sF_N

Sometimes we don’t make a distinction between static and kinetic friction, we just use a notation that assumes we are discussing kinetic friction because it is most useful to us.

F_f = mF_N

Chart on p. 144 has m values.

Example: A 91kg refrigerator is placed on a ramp. The refrigerator begins to slide when the ramp is raised to an angle of 34°. What is the coefficient of static friction?

Example: Two students are sliding a 225kg sofa at a constant speed across a wood floor. One student pulls with a force of 225N at an angle of 13° above the horizontal. The other student pushes with a force of 250N at an angle of 23° below the horizontal. What is the coefficient of kinetic friction between the sofa and the floor?