Study sheet: 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

★ Must-know

• The SI unit of work is the joule, defined as one newton-meter: $1\,\mathrm{J} = 1\,\mathrm{N}\,\mathrm{m}$.

Further detail

📐 Formula — Because work is the product of force and distance, its SI units are newtons multiplied by meters: $\mathrm{J} = \mathrm{N}\,\mathrm{m}$.

📖 4. Force–Position Graph

★ Must-know

• For a constant force, the work corresponds graphically to the area under the force-versus-position graph between the initial and final positions.

Further detail

• For a constant force from the initial position to the final position, the area under the force-versus-position graph is a rectangle whose area equals the force multiplied by the displacement.

💡 Memory Hook

The work is the shaded rectangle beneath the constant-force line