Question

1. Near the surface of the Earth, a student is using a simple pulley to lift a crate of mass M = 30 kg from rest to a height H by pulling on the rope with a constant force F as shown in the figure. If the breaking strength of the rope is 400 N, what is the minimum time (in s) required for the student to haul the crate to a height H = 20 m? (Assume that the pulley is massless and frictionless.)

2. answer is 3.4

Answer 1

a = T/m - g = 400/30 - 9.8 = 3.533 m/s^2

t = sqrt[2y/a] = sqrt[2*20/3.533] = 3.36 s

t = 3.4 s

Answer 2

Maximum force that can be applied = 400 N

So, net force on the mass = T - mg = 400 - 30 x 9.8 = 106 N

acceleration of the mass = 106 / 30 = 3.53m/s²

h = ut + 1/2 at²
$t=\sqrt{\frac{2h}{a}}\, \, \, \, \, \, \, (u=0)$
$t=\sqrt{\frac{2\times 20}{3.53}}=3.366 s$

minimum time = 3.366s= 3.4s