Physics Work & Energy UHS 2023
PMDC Verified Question 20 of 108
The work done by a variable force can be found by dividing the:
A
Force into small intervals
B
The displacement into small intervals
C
Both force and displacement into small intervals
D
By taking displacements all different angle
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: The displacement into small intervals
Concept:

When calculating work for a force that changes over a distance, we use the method of integration, which geometrically means dividing the x-axis (displacement) into infinitesimally small chunks.

Formula:

$$ W = \sum_{i} F(x_i) \Delta x_i $$

Solution:

  • If force is variable, it changes at every position.


  • We assume the force is approximately constant over a very small displacement (\( \Delta d \)).


  • Thus, we must divide the total displacement into very small intervals, calculate the tiny work \( \Delta W = F \cdot \Delta d \) for each, and sum them up.


Why other options are incorrect:

We do not divide force into intervals; force is the height (y-value) of the graph at a given displacement interval.

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