Question

The drawing shows Robin Hood (mass = 85.0 kg) about to escape from a dangerous situation. With one hand, he is gripping the rope that holds up a chandelier (mass = 240 kg). When he cuts the rope where it is tied to the floor, the chandelier will fall, and he will be pulled up toward a balcony above. Ignore the friction between the rope and the beams over which it slides, and find (a) the acceleration with which Robin is pulled upward and (b) the tension in the rope while Robin escapes.

Answer 1

Let The Tension In The Rope After The Cut Be "T"
And Acceleration Be "a"

Give Mass Of Chandelier Is 240Kg {be m'} And Of Robin Hood Is 85Kg {be m}

So Equation For Robin Hood Is As Such

T - mg = ma
=>T= ma +mg Eq. 1

Equation For Chandelier Is As Such

T - m'g = -m'a
=> T = m'g- m'a Eq. 2


Equating Equations 1 and 2 We Get

ma + mg = m'g - m'a
=> 85a+85g = 240g - 240a
=> 17a + 17g = 48g - 48a
=> 17a + 48a = 48g - 17g
=> 65a = 31g
=> a = (31/65) g Eq. 3

Putting Eq. 3 In Eq 1 we Get

T = (17 * 31/13)g + 85g

=> T = (527/13)g + 85g
=> T= (527 + 1105)g/13
=> T = 1632g/13


SO ACCELERATION IS (31/65)g NAD TENSION IS 1632g/13