Work by a Constant Force

📋 Course Outline

1. Work and Displacement
2. Sign of Work
3. Work Units
4. Force–Position Graph

📖 1. Work and Displacement

🔑 Key Concepts & Definitions

• Work: the product of a constant force and the displacement of the object in the direction of the force

★ Must-know

📐 Formula — For a constant force in the x direction, the work done from the initial position to the final position is $W = F_x\Delta x = F_x(x_{\mathrm{final}} - x_{\mathrm{initial}})$.

Further detail

• The displacement vector for motion along the x direction is $\Delta \vec{x} = \Delta x\,\hat{i}$, where $\Delta x = x_{\mathrm{final}} - x_{\mathrm{initial}}$.

💡 Memory Hook

Constant force × displacement → work

📖 2. Sign of Work

🔑 Key Concepts & Definitions

• Scalar quantity: a scalar quantity that can have a positive or negative value

★ Must-know

📌 Work is positive when the force and displacement point in the same direction and negative when the force opposes the displacement.

Further detail

• If the force component satisfies $F_x < 0$ while the displacement is positive, the work is negative.

• If both the force component and the displacement are positive, the work is positive.

💡 Memory Hook

Force with displacement: positive work; force against displacement: negative work

📖 3. Work Units