body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f8f9fa;
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
}
.calculator-container {
max-width: 700px;
margin: 30px auto;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
}
h1 {
color: #004a99;
text-align: center;
margin-bottom: 25px;
font-size: 2.2em;
}
.input-section, .result-section {
margin-bottom: 25px;
padding-bottom: 20px;
border-bottom: 1px solid #e0e0e0;
}
.input-section:last-child, .result-section:last-child {
border-bottom: none;
}
.input-group {
margin-bottom: 18px;
display: flex;
align-items: center;
flex-wrap: wrap; /* Allows wrapping on smaller screens */
}
.input-group label {
flex: 0 0 180px; /* Fixed width for labels */
margin-right: 15px;
font-weight: 600;
color: #004a99;
font-size: 1.1em;
}
.input-group input[type="number"] {
flex: 1 1 200px; /* Flexible input width */
padding: 10px 12px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
}
.input-group span {
margin-left: 10px;
font-size: 0.95em;
color: #555;
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #004a99;
color: white;
border: none;
border-radius: 5px;
font-size: 1.2em;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
button:hover {
background-color: #003366;
}
#result {
background-color: #e6f7ff; /* Light success green */
color: #004a99; /* Dark blue for contrast */
padding: 20px;
border-radius: 5px;
text-align: center;
font-size: 1.5em;
font-weight: bold;
margin-top: 20px;
border: 1px dashed #004a99;
}
#result-label {
font-size: 1.1em;
font-weight: normal;
display: block;
margin-bottom: 10px;
color: #333;
}
.article-section {
margin-top: 40px;
padding: 25px;
background-color: #f0f8ff;
border-radius: 8px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.05);
}
.article-section h2 {
color: #004a99;
text-align: center;
margin-bottom: 20px;
}
.article-section p {
margin-bottom: 15px;
}
.article-section ul {
margin-left: 20px;
margin-bottom: 15px;
}
.article-section li {
margin-bottom: 8px;
}
.formula {
font-family: 'Courier New', Courier, monospace;
background-color: #e0e0e0;
padding: 5px 10px;
border-radius: 3px;
font-size: 0.95em;
display: inline-block;
margin-bottom: 10px;
}
@media (max-width: 600px) {
.input-group {
flex-direction: column;
align-items: flex-start;
}
.input-group label {
margin-bottom: 8px;
flex: none; /* Reset flex basis */
width: 100%; /* Take full width */
}
.input-group input[type="number"] {
width: 100%; /* Take full width */
flex: none; /* Reset flex basis */
}
.input-group span {
margin-left: 0;
margin-top: 5px;
}
h1 {
font-size: 1.8em;
}
button {
font-size: 1.1em;
}
#result {
font-size: 1.3em;
}
}
Understanding Net Work
In physics, Net Work is the total work done on an object by all the forces acting upon it. It's a fundamental concept that directly relates to changes in an object's kinetic energy, as described by the Work-Energy Theorem.
The Physics Behind Net Work
Work ($W$) done by a constant force ($F$) acting on an object that undergoes a displacement ($d$) in the direction of the force is defined as:
W = F \times d
When multiple forces act on an object, we can calculate the work done by each force individually and then sum them up to find the net work, or we can calculate the resultant force (the vector sum of all forces) and then calculate the work done by this resultant force.
The Net Work ($W_{net}$) is crucial because of the Work-Energy Theorem, which states that the net work done on an object is equal to the change in its kinetic energy ($\Delta KE$):
W_{net} = \Delta KE
Kinetic energy ($KE$) is the energy an object possesses due to its motion and is calculated as:
KE = \frac{1}{2} m v^2
Therefore, the change in kinetic energy is:
\Delta KE = KE_{final} – KE_{initial} = \frac{1}{2} m v_{f}^2 – \frac{1}{2} m v_{i}^2
So, the Net Work can be directly calculated from the initial and final velocities and the mass of the object:
W_{net} = \frac{1}{2} m (v_{f}^2 – v_{i}^2)
Calculating Net Work with Non-Conservative Forces
In many real-world scenarios, non-conservative forces like friction are present. Friction always opposes motion, so the work done by friction is negative. If we know the friction force ($F_f$) acting over a distance ($d$), the work done by friction ($W_f$) is:
W_{f} = -F_{f} \times d
If other conservative forces (like gravity, where work can be accounted for by changes in potential energy) are absent or their work is accounted for, the net work can be calculated by summing the work done by all forces, including friction.
This calculator uses the Work-Energy Theorem ($W_{net} = \frac{1}{2} m (v_{f}^2 – v_{i}^2)$) and also incorporates the work done by friction if provided. If you enter friction force and distance, the calculator calculates the work done by friction and adds it to the work done calculated via kinetic energy changes.
How this Calculator Works:
- It calculates the change in kinetic energy using the initial velocity, final velocity, and mass.
- It calculates the work done by friction (if provided), which is negative as it opposes motion.
- It sums these two values to provide the total net work done on the object.
Use Cases
- Physics Education: Helping students understand the relationship between forces, motion, and energy.
- Engineering: Analyzing the energy transfer in mechanical systems, such as vehicles braking or objects being pushed.
- Sports Science: Studying the energy dynamics of athletes' movements.
- Robotics: Calculating the energy required for robotic arm movements or vehicle propulsion.
function calculateNetWork() {
var initialVelocity = parseFloat(document.getElementById("initialVelocity").value);
var finalVelocity = parseFloat(document.getElementById("finalVelocity").value);
var mass = parseFloat(document.getElementById("mass").value);
var frictionForce = parseFloat(document.getElementById("frictionForce").value);
var distance = parseFloat(document.getElementById("distance").value);
var netWorkValue = 0;
var errorMessage = "";
// Validate inputs
if (isNaN(initialVelocity) || initialVelocity < 0) {
errorMessage += "Please enter a valid non-negative initial velocity (m/s).\n";
}
if (isNaN(finalVelocity) || finalVelocity < 0) {
errorMessage += "Please enter a valid non-negative final velocity (m/s).\n";
}
if (isNaN(mass) || mass <= 0) {
errorMessage += "Please enter a valid positive mass (kg).\n";
}
if (isNaN(frictionForce) || frictionForce < 0) {
errorMessage += "Please enter a valid non-negative friction force (N). If no friction, enter 0.\n";
}
if (isNaN(distance) || distance 0 && distance > 0) {
workByFriction = -frictionForce * distance;
}
// Total Net Work is the sum of work from kinetic energy change and work by friction
netWorkValue = workFromKineticEnergy + workByFriction;
document.getElementById("netWorkValue").innerText = netWorkValue.toFixed(2);
}