Question

calculate power generated by tension in the string in first 2 seconds of motion.a man pulling a rope by which 10kg mass is hang on other side of pulley

Answer 1

Here we see body moves upward direction hence, non-inertial frame
so, use concept of pseudo force .

now F is force acting on object

F =m(g+ a)
where a =g/2 upward acceleration
F = 10( g +g/2) = 15g
if g = 10m/s²

then ,
F = 150 N
instanteous velocity (v)= u + at = 0 + gt/2
=5t
total distance covered within 0≤ t≤ 2
s = ut + 1/2gt²= 1/2g/2t² =5/2t²= (2.5)t²

now,
total energy = kinetic energy + potential energy
1/2×10(5t)² + 10×10(2.5)t²
= 250t² + 125t²
=375t²

now ,
average power = total energy /total times
=375t²/t = 375t

now put t = 2
Power = 375 × 2 =750w

Answer 2

F =m (g+ a) where a =g/2 upward increasing speed F = 10 ( g +g/2) = 15g if g = 10m/s² at that point,

F = 150 N instanteous speed (v)= u + at = 0 + gt/2 =5t add up to separate secured inside 0≤ t≤ 2 s = ut + 1/2gt²= 1/2g/2t² =5/2t²= (2.5)t² presently,

add up to vitality = active vitality + potential vitality 1/2×10(5t)² + 10×10(2.5)t² = 250t² + 125t² =375t² currently,

normal power = add up to vitality/add up to times =375t²/t = 375t presently put t = 2 Power = 375×2 =750w.