Work Power And Energy

Concept:
Physics - Conservative and Non-Conservative Forces.
Step 1: Define a non-conservative force.
A force is said to be non-conservative if the work done by or against the force in moving a body from one point to another depends on the actual path followed between those two points.
Step 2: Identify key characteristics.

• For non-conservative forces, the work done in a closed loop (returning to the start) is NOT zero.
• Common examples include Friction, Air Resistance, and Viscous drag.

Step 3: Contrast with conservative forces.
In conservative forces (like Gravity or Electrostatic forces), work is path-independent and only depends on initial and final positions. Non-conservative forces dissipate mechanical energy into other forms like heat.
Step 4: Select the matching definition.
Based on Step 1, the defining trait of a non-conservative force is that the work depends on the path.

Step 1: Use the formula for power in terms of voltage and resistance.
The power of a bulb is related to its resistance and the voltage by the formula: Thus, the resistance of each bulb can be calculated as:
Step 2: Calculate the resistance of each bulb.
Let the voltage across each bulb be . Then, the resistances of the bulbs are: - For the 10 W bulb: - For the 25 W bulb: - For the 50 W bulb:
Step 3: Use the formula for total resistance in a parallel combination.
For parallel resistors, the total resistance is given by: Substitute the values for , , and : Simplify the equation: Thus, the total resistance is:
Step 4: Calculate the total power.
The total power of the combination is given by: Substitute : Thus, the effective power of the combination is:

The work done by a force when it displaces an object through a displacement is given by: where:
- is the magnitude of the force,
- is the magnitude of the displaceent,
- is the angle between the force and the displacement vectors.
Step 1: Work and angle between force and displacement.
- When , , so work done is zero.
- When , , so work is maximum.
- When , , so work is negative.

Step 2: Area under - graph.
The work done by a force is also represented by the area under the graph of force versus displacement . This is the area under the curve on the graph, which gives the work done by the force.
Step 3: Conclusion.
Therefore, the correct statement is that the area under the - graph gives the work done, which corresponds to option (E).
Final Answer:} (E) Area under - graph gives work done

Step 1: Understanding the Concept:
Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. When the force is not constant but varies with position (as given here, ), we must use integration to calculate the work done.
Step 2: Key Formula or Approach:
The general formula for work done by a variable force from an initial position to a final position is:

Step 3: Detailed Explanation:
Given force function: N
Initial position: m
Final position: m
Set up the definite integral for work:

To evaluate this integral, find the antiderivative of . The antiderivative of is .
So, the antiderivative of is .
Now apply the limits of integration from 0 to 2:




Step 4: Final Answer:
The work done in moving the particle is 8 J.