A force of 10N acts for 20s on a body of mass 2kg initially at rest. Calculate the energy required by the body and the work done by the applied force.
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Answer:
Given Parameters;
- Force (F) = 10 N
- Initial velocity (u) = 0 m/s
- Mass (m) = 2 Kg
- Time interval (t) = 20 s
Unknown Quantities;
- Energy required by the body.
- Work done by the applied force.
Solution;
• By Newton's second law we have:
=> F = ma
=> 10 = 2a
=> a = 10 ÷ 2
=> a = 5 m/s²
• By applying first kinematical equation of motion we have:
=> v = u + at
=> v = 0 + 5 × 20
=> v = 100 m/s
•Work done by the applied force:
=> W = ∆K.E
=> W = Final kinetic energy - initial kinetic energy
=> W = ½ mv² - ½ mu²
=> W = ½ × 2 × (100)² - ½ × 2 × (0)²
=> W = 10000 J
• Energy required by the body:
=> Energy = Power × time
=> Energy = (Work done/time) × time
=> Energy = (10000/20) × 20
=> Energy = 500 × 20
=> Energy = 10000 J
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