How Much Does the Raft Rise When a 53kg Girl Dives Off?

[5.0stang]

[SOLVED] Basic Buoyant Force HW Question

First time doing this, so bare with me:)

Homework Statement

A 53kg girl dives off a raft 4m square floating in a freshwater lake. By how much does the raft rise?

Density of water = 1000kg/m^3

Use the equation for buoyant force. Then solve the equation for V.

Of course, volume = L x W x H.

g = 9.8 m/s^2

Fb = weight of girl in Newtons

The Attempt at a Solution

My teacher gives us the equation for buoyant force as Fb = (density)(volume)(acc.due to gravity).

The answer is to be given in cms (centimeters).

Fb = (1000)(?)(9.8)

I am trying to get the volume, knowing that there is 4m squared. I am just missing the height.

Thanks for any ideas...

 

[5.0stang]

Okay, just looking over my notes one more time. My teacher said to use the weight of the girl (53kg) to equal Fb.

How do I convert 53kg to Newtons? I can use online calculators, but that is not helping me learn. It looks like it is 9.8 x 53 = 519.4 Newtons

So I should be getting Fb = (1000)(V)(9.8) or 519.4 = (1000)(V)(9.8).

I just have to solve for V it looks like.

 

[5.0stang]

I am trying to solve for volume. I have 4m ^2 given in the problem.

Okay, the formula to work from is:

1. Fb = (Density in kg/m^3)(Volume)(Acc. Due to Gravity)
2. 519.4 = (1000 kg/m^3)(V)(9.8 m/s^2)
3. 519.4 = 9800V
4. Volume = 18.87 (units?)

Is this correct so far?

How do I convert this to centimeters.?

 

[Shooting Star]

I am trying to solve for volume. I have 4m ^2 given in the problem.

Okay, the formula to work from is:

1. Fb = (Density in kg/m^3)(Volume)(Acc. Due to Gravity)
2. 519.4 = (1000 kg/m^3)(V)(9.8 m/s^2)
3. 519.4 = 9800V
4. Volume = 18.87 (units?)

Is this correct so far?

How do I convert this to centimeters.?

How do you get 4 from 3?

Are you able to understand the concept behind what you are doing? Refer to this similar problem in PF and see.

https://www.physicsforums.com/showthread.php?t=214070

 

[5.0stang]

Sorry for the late response. I figured out the problem.

The professor made a typo in our question, and she corrected it. I solved it very quickly after that.

Thanks anyways!

 

[janggeng]

if Buoyant force equals to weight of girl in Newtons
Fb = W
(Density in kg/m^3)*(Volume)*(Acc. Due to Gravity) = (mass)*(Acc. Due to Gravity)
(Density in kg/m^3)*(Volume) = (mass)

Volume = A.h

(Density in kg/m^3)*(A.h) = (mass)

h = (mass) / (Density in kg/m^3)*(A) = 0.01325 m = 1,325 cm

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