Question

Identify the force present and explain whether work is being (a) You lift a book off the top performed in the following cases: of a desk. (b) Air is compressed in a bicycle pump.

Short answer

(a) The force present is the applied force (or normal force) that counters gravity acting on the book. Since the applied force and the upward displacement are in the same direction, work is being done on the book as we lift it off the desk. (b) The main force acting here is the applied force by the person compressing the pump. The air molecules' displacement occurs in the same direction as the applied force (inwards). Hence, work is being done on the air as it is being compressed inside the bicycle pump.

Step-by-step solution

Identify the forces

In this scenario, the main force acting on the book is gravity, which pulls the book downwards. When we lift the book, we are applying an upward force (called the applied force or normal force) that counters the force of gravity.

Determine the displacement

When we lift the book off the desk, it is being displaced upward. The displacement occurs in the same direction as the applied force we are applying to it.

Evaluate if work is being done

In physics, work is defined as the product of force and displacement. When a force is applied on an object and the object gets displaced in the direction of the applied force, then work is being done. In this case, since the applied force and the displacement are both in the same direction (upwards), work is indeed being done on the book as we lift it off the desk. (b) Air being compressed in a bicycle pump

Identify the forces

In this case, the main force acting is the applied force by the person who is compressing the pump. This force is directed inwards, which pushes the air molecules closer together, increasing the air pressure inside the pump.

Determine the displacement

When the air molecules are being compressed inside the pump, they experience a decrease in volume (i.e., their positions get closer together). This displacement is in the same direction as the applied force.

Evaluate if work is being done

Again, work is the product of force and displacement. In this case, the applied force and the air molecules' displacement are both in the same direction (inwards, to compress the air). Therefore, work is being done on the air as it is being compressed inside the bicycle pump.

Key concepts

Forces and Displacement

In physics, the concept of forces and displacement is very important when understanding how work is performed. To put it simply:

• A force is a push or pull acting upon an object.
• Displacement is the change in position of that object due to the force.

Both need to be considered to determine if work is done. The relationship between force and displacement is central to understanding work.
If a force is applied to an object and it moves the object in the same direction as the force, then work has occurred.
Mathematically, work (\( W \) ) can be calculated by the formula:\[ W = F \cdot d \cdot \cos(\theta) \]where:

• \( F \) is the force applied,
• \( d \) is the displacement of the object,
• \( \theta \) is the angle between the force and the displacement.

It's crucial that the force direction matches the displacement direction for maximum work. If the displacement is zero, no work is done, no matter how much force is applied. In the example of lifting a book, the force (your hand) and the displacement (movement of the book) are in the same direction, upwards.

Gravitational Force

Gravitational force is an attractive force exerted by masses towards each other. On Earth, this is commonly referred to as the weight of an object and acts downward toward the center of the planet. When discussing work and gravitational force:

• It's essential to recognize that gravity acts at all times, providing a constant force on objects.
• This force impacts how much effort is needed to move objects against its pull.

Going back to our book example, gravity pulls the book down to the desk. When you lift the book, you exert an upward force that needs to exceed gravity's downward pull for displacement to occur.
This interaction results in work being done against the force of gravity. The formula for gravitational force is:\[ F_g = m \cdot g \]where:

• \( F_g \) is the gravitational force,
• \( m \) is the mass of the object,
• \( g \) is the acceleration due to gravity (approximately \(9.81 \ m/s^2\) on Earth).

Understanding gravitational force helps explain why heavier objects require more force and result in more work when lifted.

Pressure and Compression

When you compress air in a bicycle pump, you are applying a specific force that reduces the volume of the air particles inside. This process involves:

• Applying an inward force to decrease the space between air molecules.
• Resulting in an increase in air pressure inside the pump.

Pressure is defined as force per unit area. During compression, even though the volume decreases, the pressure increases because the same amount of air is confined to a smaller space.
The work done in compressing the air is a result of the force moving against the resistance of the air compressing together. The increase in pressure is what allows pumps to effectively inflate tires or other objects. In this scenario, like with the book, work is done because:

• The internal air displacement aligns with the direction of the applied force, i.e., inwards.

Thus, understanding pressure and compression explains how work can be performed even on seemingly "incompressible" substances like air due to changes in pressure.