Mechanical Work – Educational-Animation.org

This animation illustrates the concept of mechanical work \( W = F \cdot s \) using a driving car as an example. In the work diagram, the work done appears as the area beneath the force-distance curve.

Description of the Animation

Use the accelerator pedal to speed up the car. The arrows on the vehicle show the acting forces: the driving force (blue, pointing forward), the total resistance force (red, pointing backward) and the resultant force (green), which produces the acceleration.

The middle diagram is the work diagram. It plots force against the distance travelled – the area beneath the curve equals the work done. It is split into three parts:

W_B (green) – acceleration work: it increases the car’s kinetic energy.
W_R (blue) – resistance work: it overcomes rolling and air resistance.
W_Br (red) – braking work: it occurs during full braking.

The right-hand diagram shows the velocity v and the acceleration a plotted against distance. This makes it possible to follow how the car’s motion changes while work is being done.

For a constant force, the work is simply the product of force and distance:

\[ W = F \cdot s \]

If the force changes during the journey, the work is given by the area beneath the force-distance curve:

\[ W = \int F \, ds \]

The acceleration work equals exactly the kinetic energy gained:

\[ W_B = \Delta E_{kin} = \frac{1}{2} \cdot m \cdot v^2 \]

The resistance force is made up of rolling resistance and air resistance:

\[ F_{Roll} = c_r \cdot m \cdot g \qquad F_{Air} = \frac{1}{2} \cdot \rho \cdot c_w \cdot A \cdot v^2 \]

Air resistance grows with the square of the velocity and therefore becomes the dominant resistance at high speeds.

Drive Model

The drive model selector lets you compare two cases:

Constant force: an idealised case – the driving force stays the same regardless of velocity.
Decreasing force: the more realistic model of an electric car. At low speed the force is constant; at higher speed the motor power P limits the force according to \( F = P / v \). The driving force therefore decreases as speed increases.

Physical Background

The work done by the motor splits into two parts: one part increases the car’s kinetic energy (acceleration work), the other is spent overcoming the driving resistances and is lost as heat (resistance work). During braking, the kinetic energy is removed again – the braking work converts it into heat. Overall, the principle of energy conservation holds: no energy is lost, it is only converted into other forms.