What is a Force?

Definition of Force

A force is a push or pull that has the ability to:

  • Change an object's motion (accelerate, decelerate, change direction)
  • Change an object's shape (deform)
  • Change an object's state (rest ↔ motion)

Simple Definition: A force is any interaction that tends to change the motion of an object.

Characteristics of Forces

1. Have magnitude (how strong) - Measured in Newtons (N) - Can be any positive value

2. Have direction (which way) - Specified as angle, compass direction, or relative description - Critical for vector calculations

3. Are vector quantities - Must include both magnitude and direction - Can be added vectorially - Can cancel out (equal opposite forces)

4. Require an agent (something causing the force) - Force is exerted BY an agent ON an object - Example: Wind exerts force ON a sail

The Newton (N)

The Newton is the SI unit of force.

$$ 1 \text{ Newton (N)} = 1 \text{ kg} \times \text{m/s}^2 $$

Definition: One Newton is the force required to accelerate a 1 kg mass at 1 m/s².

Context for understanding:

  • Weight of 100 g object ≈ 1 N
  • Weight of 1 kg object ≈ 10 N
  • Weight of 10 kg object ≈ 100 N

Effects of Forces

1. Changing Motion

A force can:

  • Start an object moving (from rest → motion)
  • Stop moving objects (from motion → rest)
  • Speed up objects (increase velocity)
  • Slow down objects (decrease velocity)
  • Change direction (curve path, turn)

Key Concept: The greater the force, the greater the change in motion.

2. Deforming Objects

A force can:

  • Stretch (tension force)
  • Compress (compression force)
  • Bend (bending force)
  • Twist (torsion force)

Examples:

  • Stretching a rubber band
  • Compressing a spring
  • Bending a ruler
  • Twisting a towel

3. Changing State

A force can:

  • Create rotation (torque)
  • Create pressure (concentrated force over area)
  • Cause friction (when surfaces interact)

Types of Force Interactions

Direct Contact vs. Distant Action

Contact Forces

Forces that require physical contact between objects:

  • Friction (sliding surfaces)
  • Normal force (pushing against surface)
  • Tension (pulling with rope)
  • Applied force (pushing with hand)

Non-Contact Forces

Forces that act over a distance without touching:

  • Gravitational force (planets, objects falling)
  • Magnetic force (magnets, Earth's magnetism)
  • Electric force (charged particles)

Force Diagrams (Free Body Diagrams)

What is a Free Body Diagram?

A Free Body Diagram (FBD) is a drawing showing:

  • The object of interest as a point or simple shape
  • All forces acting on that object
  • Nothing else (no other objects)

Drawing FBDs

Rules: 1. Draw the object as a simple dot or square 2. Draw each force as an arrow 3. Arrow direction = force direction 4. Arrow length proportional to force magnitude 5. Label each force with symbol and value 6. Include coordinate system (x, y axes)

Example FBD: Book on Table

For a book resting on a table:

  • Weight (W): Arrow pointing downward
  • Normal force (N): Arrow pointing upward
  • Equal and opposite: W = N
  • Net force: Zero (book at rest)

Example FBD: Sliding Block

For a block sliding on a floor:

  • Weight (W): Downward
  • Normal force (N): Upward
  • Friction (f): Opposite to motion
  • Applied force (F): Direction of push/pull
  • Net force: F − f = ma

Net Force and Resultant

What is Net Force?

Net force is the vector sum of all forces acting on an object.

$$ \vec{F}_{\text{net}} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + ... $$

Calculating Net Force

Same Direction

Forces in the same direction add:

$$ F_{\text{net}} = F_1 + F_2 $$

Example: Two people pushing same direction: 50 N + 30 N = 80 N

Opposite Direction

Forces in opposite directions subtract:

$$ F_{\text{net}} = |F_1 - F_2| $$

Example: Two people pulling opposite: 50 N − 30 N = 20 N (in direction of 50 N)

Perpendicular Forces

Use Pythagorean theorem:

$$ F_{\text{net}} = \sqrt{F_1^2 + F_2^2} $$

Example:

  • F₁ = 30 N (horizontal)
  • F₂ = 40 N (vertical)
  • F_net = √(30² + 40²) = √(900 + 1600) = 50 N

Equilibrium

An object is in equilibrium when the net force is zero:

$$ \vec{F}_{\text{net}} = 0 $$

States of equilibrium: 1. Static equilibrium: At rest (v = 0) 2. Dynamic equilibrium: Constant velocity motion (v = constant)

Example: A car traveling at constant speed has net force = 0 (engine force = friction force)

Force and Acceleration

Newton's Second Law of Motion

$$ F_{\text{net}} = ma $$

Interpretation:

  • Acceleration is directly proportional to net force
  • Acceleration is inversely proportional to mass
  • Doubling force doubles acceleration
  • Doubling mass halves acceleration

Common Force Scenarios

Pulling or Pushing

A force applied to an object causes acceleration:

$$ F = ma $$
$$ a = \frac{F}{m} $$

Friction Opposing Motion

Net force is reduced by friction:

$$ F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} $$
$$ ma = F_{\text{applied}} - \mu mg $$

Weight and Falling Objects

On Earth, gravity causes acceleration:

$$ W = mg = 9.8m $$

Free fall acceleration (no air resistance):

$$ a = g = 9.8 \text{ m/s}^2 $$

Measuring Forces

Spring Scale

  • Uses Hooke's Law (F = kx)
  • Spring stretches proportional to force
  • Marked in Newtons

Force Sensors

  • Electronic devices measuring force
  • Used in modern physics labs
  • Can measure very small or very large forces

Indirect Measurement

Using F = ma:

  • Measure mass and acceleration
  • Calculate force

Combining Multiple Forces

When multiple forces act on an object:

1. Draw a free body diagram 2. Resolve forces into components (if at angles) 3. Sum forces in each direction 4. Calculate net force using Pythagorean theorem if needed 5. Apply Newton's laws to find acceleration or equilibrium

Example: Combined Forces

A 10 kg object has:

  • Applied force: 50 N (right)
  • Friction: 20 N (left)
  • Weight: 100 N (down)
  • Normal: 100 N (up)

Horizontal: F_net = 50 − 20 = 30 N (right) Vertical: F_net = 100 − 100 = 0 N Overall net force: 30 N (right) Acceleration: a = 30/10 = 3 m/s² (right)

Real-World Applications

Transportation

  • Braking: Friction force slows vehicle
  • Acceleration: Engine force propels vehicle
  • Turning: Friction provides centripetal force

Sports

  • Throwing: Applied force accelerates ball
  • Catching: Friction stops ball (distributed over time)
  • Jumping: Leg force overcomes weight

Engineering

  • Bridges: Calculate forces on supports
  • Buildings: Design for weight and wind forces
  • Machines: Optimize force and motion

Space

  • Rockets: Thrust force for acceleration
  • Orbits: Gravity provides centripetal force
  • Weightlessness: No normal force (free fall)

Key Takeaways

1. Force = push or pull; vector quantity with magnitude and direction 2. Unit: Newton (N) = kg⋅m/s² 3. Effects: Change motion, deform objects, create rotation 4. Net force = vector sum of all forces 5. Equilibrium: Net force = 0 (at rest or constant velocity) 6. Newton's 2nd Law: F_net = ma 7. Free Body Diagrams: Show all forces on object 8. Contact vs. non-contact forces exist in nature

1. What is the SI unit of force? (1 points)

2. What is a force? (1 points)

3. What is a Free Body Diagram? (1 points)

4. According to Newton's Second Law, if force is constant but mass doubles, acceleration: (1 points)

5. What is net force? (1 points)

6. When is an object in equilibrium? (1 points)

7. What are contact forces? (1 points)

8. Which of the following is a non-contact force? (1 points)

9. If two forces of 30 N (right) and 20 N (left) act on an object, the net force is: (1 points)

10. What does it mean if an object has zero acceleration? (1 points)

11. Force calculations: (4 points)

a ) A 5 kg object experiences a net force of 20 N. Its acceleration = _____ m/s² (Using F = ma)

b ) A 2 kg ball is accelerated at 6 m/s². The force required = _____ N

c ) Two perpendicular forces: F₁ = 30 N, F₂ = 40 N. Net force = _____ N (Use Pythagorean theorem)

d ) Three forces act on object: 50 N (right), 30 N (left), 20 N (left). Net force = _____ N

12. Force effects and characteristics: (2 points)

a ) What two properties must every force have? Answer with two words separated by 'and': _____

b ) A book resting on a table is in equilibrium because the net force equals _____ (Answer: zero or 0)