Tension and Rolling a sphere(Very Detailed, though)

[tcin06]

1. How much tension exists in each of two cables used to lower a 10m 500 kg gang plank to horizontal if the cables originate 2 meters above the planks hinges on the ship


Relevant equations
Moment of Inertia (Does it apply?)
Torque Equilibrium (I'm so lost that I don't even know if torques involved)
Pythageron Theroem Possibly?
No Angles are given


The attempt
My only idea was to figure out the torque on the whole system. T=Fd
F=m(500kg)*g
D=10 m
Multiplying that out gives me 49,050 N, divide by 2 since there are two cables to get the tension of each cable
I don't think this is right because the 2 meter part of the problem isn't used.
This ones got me tripping. please help


2. You want to roll a 2 m beryllium sphere 10 meters while speeding it up from rest to a velocity of 103 m/s. The density of Be is 1848 kg/m^3
Find
A) How much work would this take?
B) What force would be required?
C) How much force was required to do the translational work?
D) Rotational?
E) How much time did this take?

relevant Equations
I=2/5MR2
W=V/R
T=D/V
Torque=Fd
Net Torque=I*angular acceleration

Attempted Solution
The first step i took was changing the velocity and acceleration into their angular versions. So i took the radius of the sphere..1(correct?). W=103/1=103 rad/s, Ang. Acc=103m/s2/1=103 rad/s2 From there i tried to find the time (e). T=D/V, 10/103 rad/s=.09s

I was going to calcuate I but i can't find the mass. How do you take the density of the element in order to find that spheres mass? It makes no sense to me, without I i can't calculate net torque which i assumed would answer part B (what force is required), without part b i can't get part a, (work) which is f*d, and without either of those i can't split up the forces into their rotational and translational parts which I am confused on anyways.


Please help I've worked on these for a few hours today, their part of a huge packet that's due tommorow and these are the 2 i have left. I've googled different parts of the questions to get hints but I'm completely lost on how to approach these and what to do.

Thanks

 

[member 553083]

in advance!Answer to question 1: The tension in each of the two cables is equal to the weight of the gang plank (500 kg) multiplied by the acceleration due to gravity (9.8 m/s2). Therefore, each cable will have a tension of 4900 N. To calculate the tension at the point of origin (2 m above the plank's hinges), you can use the Pythagorean theorem to calculate the hypotenuse of the triangle formed by the two cables. The tension at the origin would then be equal to the hypotenuse multiplied by the weight of the plank.