Calculating Tension in Anchor Cord for Submerged Box

[lenarass]

tension, forces .please help me:(

Homework Statement

A hollow but water-tight cubic box of wood, 1.2m on each side, weighs 961 N in air. It is placed in fresh water lake tied to an anchor made of solid iron (1m x 1m x 10 cm) with a weightless cord of such length that exactly half of the wooden box is submerged. What is the tension in the cord?

Homework Equations

i don't know how to start.if u can help me a little bit and then try together i will appreciate it!:)

The Attempt at a Solution

sorry:( i just need a little bit help

 

[kuruman]

Start by drawing a free body diagram of the box showing all the forces acting on it. How many are there and in what direction does each force act? What is the net force on the box?

 

[lenarass]

i did that but then? i don't know ..thx for helping me kuruman
why it says bout volume of anchor. why it gives me the dimension of each side of the box? (1.2)
how do u use them:/

 

[Rajini]

when you tie you object/wood in air it weighs 961 N. That means the tension on the rope is 961 N. Now you find the same when the wood is tied to solid iron, and also when it is immersed in water...that is all you need...just apply buoyancy + Archimedes rule..
good luck

 

[kuruman]

i did that but then? i don't know ..thx for helping me kuruman
why it says bout volume of anchor. why it gives me the dimension of each side of the box? (1.2)
how do u use them:/

What is the buoyant force according to Archimedes' principle?

 

[lenarass]

Volume of cube = 1.2^3 = 1.728 m^3

then divide by 2 because the cub is half in water so 1.728/2= 0.864 m^3

water displaced => m (mass) = V(volume) * p (density of water)
so

0.864 x 1000 = 864 kg

864 x 9.8 = 8467.2 N

so apparent weight of cube is 961 - 8467.2 = -7506.2 N

so tension in cord is -7506.2 N ?? ?

 

[Rajini]

negative value means compression!
What happened to the iron solid?? include that also

 

[lenarass]

negative value means compression!
What happened to the iron solid?? include that also

what do u mean? should i include volume of anchor also? that's why he gave me its dimensios?

 

[Rajini]

Hmm if i understand your case..the wood and iron block were tied with a string. And you want to find the tension in that string ?...I such case i assume iron block does not hit the ground..if it hits then no tension in that string..so just find the buoyant force for wood and anchor separately..and buoyant force acts upwards..so find the difference..buoyant for for wood is high because it float top and anchor bottom..
do you have a solution for you question?
PS: forgot to inform you..in both cases include 961 N!