Faculty Key · Work by a Variable Force & Hooke’s Law
Complete solutions, method expectations, validity conditions, and verification guidance.
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Khaemenes Higher Learning
Faculty Key · Work by a Variable Force & Hooke’s Law
Show method selection, derivation, conditions, units, verification, and interpretation.
U07 · L01
Name
Date
1
State the central method of Work by a Variable Force & Hooke’s Law and list the conditions that must be checked.
Faculty solution: Use integrating force over displacement. State the relevant hypotheses, domain or interval, units when applicable, and a verification plan.
2
A spring with k=20 N/m is stretched from 0.1 m to 0.3 m. Find work.
Faculty solution: ∫_.1^.3 20x dx=0.8 J.
3
A variable force F(x)=x²+1 moves an object 0≤x≤2.
Faculty solution: W=∫₀²(x²+1)dx=14/3 J.
4
A learner makes an error by dropping density, pressure, probability, or physical units. Explain the first invalid step and repair the reasoning.
Faculty solution: The first invalid step is dropping density, pressure, probability, or physical units. Return to the governing definition or theorem, restore the missing condition, and verify the corrected result.
5
Create a short application of Work by a Variable Force & Hooke’s Law in mechanical work, fluids, structures, reliability, and probabilistic decision-making. Define variables and identify the quantity an integral, differential equation, sequence, or series would measure.
Faculty solution: A defensible response defines variables and units, states assumptions, builds the correct mathematical object, and interprets its value in mechanical work, fluids, structures, reliability, and probabilistic decision-making.
6
Describe two independent ways to verify a result from Work by a Variable Force & Hooke’s Law.
Faculty solution: Use an exact structural check such as differentiation, substitution, partial sums, or theorem hypotheses; then compare with numerical, graphical, dimensional, or limiting evidence.