105.Forces

Core + ExtendedIGCSE 0625

1. What is a Force?

A force is essentially a push or a pull acting on an object resulting from its interaction with another object.

Forces are Vector Quantities: This means they have both magnitude (size) and direction. A 10 N force to the right is completely different from a 10 N force to the left.

Effects of a Force:

- Change Speed: Accelerate (speed up) or Decelerate (slow down).

- Change Direction: Make a moving object turn.

- Change Shape: Stretch, compress, or deform an object.

Forces as Vectors

2. Contact Forces

Contact forces occur when two objects are physically touching each other. The force is transmitted through the point of contact.

Types of Contact Forces

3. Non-Contact Forces

Non-contact forces (or action-at-a-distance forces) act on an object without needing any physical contact. They act through a 'field'.

Forces acting at a Distance

4. Resultant Force (Net Force)

In reality, mostly more than one force acts on an object. The Resultant Force is a single force that has the same effect as all the individual forces combined.

Rules for Combination:

1. Same Direction: ADD the forces. F_resultant = F₁ + F₂

2. Opposite Direction: SUBTRACT the smaller from the larger. F_resultant = F_larger - F_smaller

3. Perpendicular Forces: Use Pythagoras theorem R² = A² + B² and trigonometry for direction.

Calculating Resultant Force

5. Newton's First Law

Newton's First Law states: An object will remain at rest or generally continue to move at a constant velocity unless acted upon by a resultant force.

Inertia: This is the natural tendency of an object to resist changes in its motion. An object with more mass has more inertia.

• If Resultant Force = 0: Velocity is constant (a = 0).

• If Resultant Force ≠ 0: The object will accelerate.

Inertia in Action

6. Newton's Second Law

Newton's Second Law: The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass.

Formula: $F = m a$

- F: Resultant Force (N)

- m: Mass (kg)

- a: Acceleration (m/s²)

This means a larger force causes a larger acceleration, but a larger mass makes it harder to accelerate.

F = ma Visualized

Tip

What the gradient means

On a Force vs Acceleration graph, the gradient is the mass (because $F = m a$ ). A steeper line means a larger mass.

Warning

Resultant force, not just applied force

Always use the resultant (net) force. If friction/drag acts, the engine force is NOT the same as the net force.

Graph 1: Force vs Acceleration (constant mass)

Straight line through the origin. Gradient = mass $m$ . Doubling the force doubles the acceleration.

Graph 2: Acceleration vs Force (constant mass)

Straight line through the origin. Gradient = $1 / m$ . For a heavier object, the line is less steep.

Graph 3: Acceleration vs Mass (constant force)

Inverse curve: $a = \frac{F}{m}$ . As mass increases, acceleration decreases (for the same resultant force).

Worked Examples

A resultant force of 500 N acts on a 50 kg object. Calculate the acceleration.

Solution

Given: F = 500 N, m = 50 kg

Rearrange Newton's Second Law:

F = m a

a = \frac{F}{m}

Substitute values:

a = \frac{500}{50} = 10 {m/s}^{2}

Explanation: The larger the force applied, the greater the acceleration. Since the object is 50 kg, a 500 N force causes it to accelerate at 10 m/s². If the mass were doubled to 100 kg with the same force, the acceleration would only be 5 m/s².

A car of mass 1200 kg accelerates at 2 m/s². Calculate the resultant force acting on the car.

Solution

Given Information:

- Mass (m) = 1200 kg

- Acceleration (a) = 2 m/s²

- Find: Resultant Force (F)

Step 1: Identify the Formula

Newton's Second Law states:

F = m a

Step 2: Substitute Values

F = 1200 \times 2

Step 3: Calculate

F = 2400 N

Physical Interpretation:

- The 1200 kg car experiences a net force of 2400 N pushing it forward

- This force overcomes air resistance and rolling friction

- The same force on a lighter 600 kg car would produce 4 m/s² acceleration

- The same force on a heavier 2400 kg truck would produce only 1 m/s² acceleration

Real-world Context: This is the NET force. The engine produces more force, but friction and air resistance reduce the net effect to 2400 N.

A force of 180 N produces an acceleration of 6 m/s² on an object. Calculate the mass of the object.

Solution

Given Information:

- Force (F) = 180 N

- Acceleration (a) = 6 m/s²

- Find: Mass (m)

Step 1: Start with Newton's Second Law

F = m a

Step 2: Rearrange to Solve for Mass

Divide both sides by acceleration:

m = \frac{F}{a}

Step 3: Substitute Values

m = \frac{180}{6}

Step 4: Calculate

m = 30 kg

Physical Interpretation:

- A 180 N force accelerates a 30 kg mass at 6 m/s²

- If the mass were doubled to 60 kg, the same 180 N force would only accelerate it at 3 m/s²

- If the mass were halved to 15 kg, the same force would accelerate it at 12 m/s²

- Mass is inversely proportional to acceleration (heavier objects need more force for same acceleration)

Check: F = ma = 30 × 6 = 180 N ✓

A 500 kg lift (elevator) is lifted vertically upward with an acceleration of 2 m/s². Calculate: (a) The tension in the cable, (b) The net force on the lift. (Take g = 10 m/s²)

Solution

Given Information:

- Mass of lift (m) = 500 kg

- Upward acceleration (a) = 2 m/s²

- Gravitational field strength (g) = 10 m/s²

- Find: (a) Tension (T) and (b) Net Force (F)

Step 1: Calculate the Weight of the Lift

Weight is the gravitational force acting downward:

W = m g

W = 500 \times 10 = 5000 N

Step 2: Identify Forces Acting on the Lift

- Tension (T): Cable pulls UP (positive direction)

- Weight (W): Gravity pulls DOWN (negative direction)

- Net Force: F = T - W (upward, causing upward acceleration)

Step 3: Apply Newton's Second Law

The net upward force causes upward acceleration:

F_{n e t} = T - W = m a

Part (a): Calculate Tension

T - W = m a

T - 5000 = 500 \times 2

T - 5000 = 1000

T = 5000 + 1000

T = 6000 N

Part (b): Calculate Net Force

F_{n e t} = m a

F_{n e t} = 500 \times 2

F_{n e t} = 1000 N

7. Newton's Third Law

Newton's Third Law states: Whenever two objects interact, they exert equal and opposite forces on each other.

Key Features:

1. Forces occur in pairs (Action & Reaction).

2. They are equal in magnitude but opposite in direction.

3. Crucially, they act on DIFFERENT objects.

Example: When you sit on a chair, your body pushes down on the chair (Action), and the chair pushes up on your body (Reaction).

Action-Reaction Pair

8. Equilibrium

Equilibrium occurs when the resultant force on an object is zero.

This concept implies:

1. No Acceleration: The object's velocity is constant.

2. State: The object is either at rest OR moving in a straight line at a constant speed.

Crucial Point: Equilibrium ≠ Stationary. A car moving at 100 km/h constant velocity is in equilibrium because the driving force equals the drag force.

105.Forces

1. What is a Force?

Forces as Vectors

2. Contact Forces

Types of Contact Forces

3. Non-Contact Forces

Forces acting at a Distance

4. Resultant Force (Net Force)

Calculating Resultant Force

5. Newton's First Law

Inertia in Action

6. Newton's Second Law

F = ma Visualized

Graph 1: Force vs Acceleration (constant mass)

Graph 2: Acceleration vs Force (constant mass)

Graph 3: Acceleration vs Mass (constant force)

Worked Examples

Solution

Solution

Solution

Solution

7. Newton's Third Law

Action-Reaction Pair

8. Equilibrium

Equilibrium States