2. Force, Torque, and Work

Force

Interaction that causes an object to accelerate

Newton (N)

Unit of force; 1 N = kg*m/s² (amount of force necessary to accelerate 1 kg by 1 m/s²)

4 Natural Forces:

1. Gravitational

2. Electromagnetic

3. Strong Nuclear Force

4. Weak Nuclear Force

Gravitational Force (F_g)

Force exerted by gravity on mass at a distance

Electromagnetic Force (F_E)

Electrostatic force

Contact Force

Force exerted when objects are touching (Normal and friction forces)

Normal Force (F_N)

Force acting perpendicular to surface, preventing object from passing through it

Friction Force (f)

Force that acting parallel to surface, that the surface exerts on an object trying to slide across it

Tension Force (F_T)

Force exerted by ideal string, allowing contact/pushing forces exerted at a distance (pulley)

Centripetal Force (F_c)

Force acting on an object, causing it to move in a circular path

Spring/Elastic Force (F_s)

Force exerted by spring or elastic material when it is stretched or compressed; Follows Hooke’s Law (F_s = -kx)

Newton’s Laws

1. Law of Inertia

2. Sum of Forces = mass x acceleration

3. Equal and Opposite Forces

Newton’s First Law

An object at motion/rest will stay in motion/rest unless acted upon by an outside force (F_net = 0 at equilibrium)

Newton’s Second Law

The sum of forces = ma (F_net = ma)

Newton’s Third Law

Forces come in pairs; F_AB = -F_BA (equal and opposite forces)

Free Body Diagrams

Representation of all forces acting on an objects

f_k =

μ_kF_N (μ_k = kinetic friction constant)

f_s =

μ_sF_N (μ_s = static friction constant)

Center of Mass (x_center) =

(x₁m₁ + x₂m_2…)/(m₁ + m₂…)

Static Friction

Friction force preventing an object at rest from moving (pushing a box and it not moving)

Kinetic Friction

Friction force acting on moving object, trying to stop it from moving (after you’ve gotten the box to move)

If a force is applied to an object but doesn’t move:

F_app < F_max

What are kinetic and static coefficients dependent on?

Each material-surface pairing

Key point to kinetic and static friction:

More force is needed to get an object to move than is needed to keep that object in motion (overcoming static harder than overcoming kinetic friction)

Air Resistance (Drag)

Opposes motion of moving object by v²; affected by 4 factors

4 Factors Affecting Drag

1. Air density (medium)

2. Object velocity (v²)

3. Object cross-sectional area

4. Drag coefficient (based on object properties)

When drag = gravitational force…

Terminal velocity has been reached; object stops accelerating

For boxes on incline, g_x is always…

gsinθ (parallel)

Pulleys

Include tensions forces to allow angle force is transmitted through to change

How to solve pulley questions:

1. Draw FBDs for each mass on the pulley

2. Tension force always points up to pulley, opposing gravity

3. The forces acting on the two masses should be the same

4. Think of the two masses as the same (m₁+m₂)

5. Only the gravitational force magnitudes matter

Gravity

Attraction between objects that have mass

F_{gravitational} =

(G*m₁m₂)/r² (Ex. Sun and Earth in circular motion)

Outside Earth instantaneous velocity is…

Perpendicular to the force of gravity

Hooke’s Law

F_s = -kx

k = spring constant (N*m)

x = amount stretched/compressed

A higher spring constant (k) means…

The spring is stiffer; requires more force to stretch/compress

Torque

Rotational force (often applied to lever at a distance away from object)

Fulcrum

Point around which an object rotates

τ (torque) =

F*dsinθ (N*m)

d = distance between fulcrum and applied force

θ between lever arm and force

To achieve the most torque…

Apply force perpendicular and as far from fulcrum as possible

Think of torque rotation as…

Clockwise or counterclockwise

Energy

What accomplishes work (Joules, 1 N*m = kg*m/s²)

Work =

Fdcos(θ) (Joules, kg*m/s²)

Conservative Forces

Path-independent (displacement)(work done by conservative force doesn’t rely on path); F_g, F_E, F_s

Non-conservative Forces

Rely on distance or path; friction, air resistance

Force vs. distance Graph

Area under curve = Work

Why is moving an object up and down have W = 0?

Because displacement is 0 (returning to start position)

Mechanical Advantage

Being apply to apply less force than usually needed by using a different apparatus (seesaw); NOT do less work

What will have mechanical advantage?

The device/method that needs less force but does same work

Mechanical advantage =

Length of incline/height of incline (pushing vs pulling up)

Power =

Work/Δt (Watt or J/s) = F*v ← only used in some cases

Power

How quickly work can be expended (quicker = more power)