Forces: Scalar and Vector Quantities

This section explains forces: scalar and vector quantities, covering, contact and non-contact forces, gravity, weight calculation formula, resultant forces and work done and energy transfer. 

Scalar Quantities

A scalar quantity only has magnitude (size) and does not have a direction. Examples include:

• Distance
• Speed
• Time
• Mass
• Temperature

Vector Quantities

A vector quantity has both magnitude (size) and direction. Examples include:

• Displacement
• Velocity
• Force
• Acceleration

Forces

A force is a vector quantity and is a push or pull on an object that can cause it to change its motion. Forces can cause objects to:

• Accelerate
• Decelerate
• Change shape
• Change direction

The unit of force is the Newton (N).

Contact and Non-Contact Forces

Contact forces are forces that require two objects to be in physical contact with each other. These forces occur when objects push or pull on one another directly. Examples of contact forces include friction, which resists the movement of objects sliding past each other; tension, the force exerted by a stretched object like a rope or spring; air resistance, which slows down objects moving through the air; and normal force, which acts perpendicular to a surface to support an object resting on it.

On the other hand, non-contact forces act at a distance without the need for physical contact between objects. These forces include gravitational force, which pulls objects towards each other, such as the Earth’s gravity pulling objects towards the ground; electrostatic force, which acts between charged particles; and magnetic force, which affects magnetic materials or other magnets without direct contact. Non-contact forces are fundamental to understanding how objects interact over a distance, like how the Earth keeps the Moon in orbit.

Gravity

Gravity is a force that attracts objects towards the centre of the Earth (or any other planet). The force of gravity gives objects weight.

• Gravitational field strength near the Earth’s surface is approximately 9.8 N/kg.
• The force of gravity acting on an object is called its weight.

Weight Calculation Formula

The weight (W) of an object can be calculated using the formula:

$$\text{Weight (W)} = \text{Mass (m)} \times \text{Gravitational field strength (g)}$$ 

Where:

• W is the weight in Newtons (N).
• m is the mass in kilograms (kg).
• g is the gravitational field strength, typically 9.8 N/kg on Earth.

Example:

If an object has a mass of 5 kg, its weight can be calculated as follows:

$$W = m \times g$$

$$W = 5 \, \text{kg} \times 9.8 \, \text{N/kg}$$

$$W = 49 \, \text{N}$$ 

So, the weight of the object is 49 N.

Resultant Forces

When multiple forces act on an object, the resultant force is the single force that has the same effect as all the individual forces combined. The resultant force can be found by:

• Adding forces that act in the same direction.
• Subtracting forces that act in opposite directions.

If the resultant force is zero, the object is in a state of equilibrium (no change in motion). If the resultant force is non-zero, the object will accelerate in the direction of the resultant force.

Work Done and Energy Transfer

Work done is the transfer of energy when a force acts on an object and causes it to move. If an object does not move, no work is done, even if a force is applied.

Work Done Formula

The formula to calculate work done is:

$$\text{Work Done (W)} = \text{Force (F)} \times \text{Distance (d)} \times \cos(\theta)$$ 

Where:

• W is the work done in joules (J).
• F is the force applied in Newtons (N).
• d is the distance moved in the direction of the force in metres (m).
• θ is the angle between the direction of the force and the direction of movement.

Example:

A force of 10 N is applied to push an object for a distance of 5 m in the same direction as the force. The work done is calculated as:

$$W = F \times d$$

$$W = 10 \, \text{N} \times 5 \, \text{m}$$

$$W = 50 \, \text{J}$$

So, the work done is 50 joules (J).

Forces are vectors and can cause objects to accelerate, decelerate, or change direction. The weight of an object is the force due to gravity, and its magnitude can be calculated using the formula $W = m \times g$. Resultant forces determine the overall effect of multiple forces acting on an object, and work done refers to the transfer of energy when a force causes an object to move. Understanding these concepts is crucial for mastering forces in GCSE Physics.