What is represented by the product of force with displacement in the direction of force?
Work
Understanding the Concept of Work in Physics
The question asks to identify the physical quantity that is defined as the product of force and the displacement in the direction of the force. This is a fundamental definition in physics related to energy transfer.
Defining Work Done by a Force
In physics, work is done by a force when it causes a displacement of an object. Specifically, if a constant force $\vec{F}$ acts on an object and causes a displacement $\vec{d}$, the work $W$ done by the force is given by the dot product of the force and displacement vectors:
$$W = \vec{F} \cdot \vec{d}$$
If the force $\vec{F}$ is acting in the same direction as the displacement $\vec{d}$, the angle between them is $0^\circ$, and $\cos(0^\circ) = 1$. In this specific case, the magnitude of the work done simplifies to:
$$W = |\vec{F}| |\vec{d}| \cos(0^\circ) = Fd$$
where $F$ is the magnitude of the force and $d$ is the magnitude of the displacement. This matches the description in the question: the product of force with displacement in the direction of force.
Analyzing the Given Options
Let's look at the other options provided and see why they do not match the definition given in the question:
- Momentum: Momentum ($\vec{p}$) is a measure of the mass in motion. It is defined as the product of an object's mass ($m$) and its velocity ($\vec{v}$).
$\vec{p} = m\vec{v}$
The unit of momentum is kg·m/s. It is not defined as force times displacement. - Impulse: Impulse ($\vec{J}$) is the change in momentum of an object. It is also defined as the product of the average force ($\vec{F}_{avg}$) acting on an object and the time interval ($\Delta t$) over which the force acts.
$\vec{J} = \vec{F}_{avg} \Delta t = \Delta \vec{p}$
The unit of impulse is Newton-second (N·s) or kg·m/s. It is related to force and time, not force and displacement. - Work: As defined above, work ($W$) is the product of force and displacement in the direction of the force. The unit of work is Joule (J). This definition perfectly matches the question.
- Power: Power ($P$) is the rate at which work is done or energy is transferred. It is defined as work ($W$) divided by the time interval ($\Delta t$) over which the work is done.
$P = \frac{W}{\Delta t}$
The unit of power is Watt (W), which is Joules per second (J/s). It is related to work and time, not directly force and displacement as a product.
Comparison of Physical Quantities
Here is a quick comparison of the relevant quantities:
| Quantity | Definition/Formula | Units | Relation to Force |
|---|---|---|---|
| Work | Force × Displacement (in direction of force) or $\vec{F} \cdot \vec{d}$ | Joules (J) | Product of force and displacement |
| Momentum | Mass × Velocity or $m\vec{v}$ | kg·m/s | Related via impulse (change in momentum) |
| Impulse | Force × Time Interval or $\vec{F}_{avg} \Delta t$ | N·s or kg·m/s | Product of force and time |
| Power | Work ÷ Time Interval or $P = \frac{W}{\Delta t}$ | Watts (W) or J/s | Rate of doing work |
Based on the definitions, the product of force with displacement in the direction of force uniquely represents Work.
Revision Table: Key Concepts Review
| Concept | Definition | Formula |
|---|---|---|
| Work | Energy transferred by a force over a distance | $W = Fd \cos\theta$ (where $\theta$ is angle between $\vec{F}$ and $\vec{d}$) |
| Momentum | Quantity of motion of a moving body | $\vec{p} = m\vec{v}$ |
| Impulse | Change in momentum; effect of force over time | $\vec{J} = \vec{F}_{avg} \Delta t$ |
| Power | Rate of doing work | $P = W/t$ |
Additional Information: Work and Energy
Work is closely related to energy. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Work is a scalar quantity, although it is calculated from vector quantities (force and displacement). Positive work is done when the force has a component in the direction of displacement, increasing the object's energy. Negative work is done when the force has a component opposite to the displacement, decreasing the object's energy. Zero work is done if there is no displacement or if the force is perpendicular to the displacement.
Important Questions from Work Power Energy
The energy possessed by a body due to its change in position or shape is called
Wind turbines convert ________ energy into mechanical power.
The rate of doing work is called:
What powers the Earth's internal heat engine?
What is the commercial unit of electric energy?
