A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance of 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

Question

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance of 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box? (A) 5690 J (B) 5250 J (C) 3280 J (D) 2780 J

Tardigrade Admin · Accepted Answer

F =200 N for 0 ≤ x ≤ 15 =200-(100/15)( x -15) for 15 ≤ x <30 W =∫ F dx =∫ limits015 200 dx +∫ limits1530(300-(100/15) x ) dx =200 × 15+300 × 15-(100/15) × ((302-152)/2) =3000+4500-2250 =5250 J

5690 J

5250 J

3280 J

2780 J

F=200N for 0≤x≤15 =200−15100​(x−15) for 15≤x<30 W=∫Fdx =0∫15​200dx+15∫30​(300−15100​x)dx =200×15+300×15−15100​×2(302−152)​ =3000+4500−2250 =5250J

$F = 200 N$ for $0 \leq x \leq 15$
$= 200 - \frac{100}{15} (x - 15)$ for $15 \leq x < 30$
$W = \int F d x$
$= 0 \int 15 200 d x + 15 \int 30 (300 - \frac{100}{15} x) d x$
$= 200 \times 15 + 300 \times 15 - \frac{100}{15} \times \frac{( 3 0 ^{2} - 1 5 ^{2} )}{2}$
$= 3000 + 4500 - 2250$
$= 5250 J$