The greater the change in velocity, or speed.
Given :
An object with a volume of 9 cm³ is completely submerged in the water.
To Find :
How much water is displaced by the object.
Solution :
According to Archimedes' principle, the amount of volume displaced of fluid when an object is fully and partially submerged into that is equal to the volume of the object below the surface of liquid.
Now, it is given that object is fully submerged into water.
Therefore, volume of water displaced by the object is 9 cm³.
To solve this problem we will use the work theorem which describes the change of force in proportion to the distance traveled.
Our function is given as:
![F_{ax} = 8x-5x^2](https://tex.z-dn.net/?f=F_%7Bax%7D%20%3D%208x-5x%5E2)
PART A) The maximum work is given in the position in which the function of the Force is equal to zero, therefore
![F_{ax} = 0](https://tex.z-dn.net/?f=F_%7Bax%7D%20%3D%200)
![8x-5x^2 = 0](https://tex.z-dn.net/?f=8x-5x%5E2%20%3D%200)
![8= 5x](https://tex.z-dn.net/?f=8%3D%205x)
![x = 1.6m](https://tex.z-dn.net/?f=x%20%3D%201.6m)
PART B) The maximum work done is given from the 0 position to the maximum work distance, therefore:
![W = \int^{1.6}_0 (8x-5x^2)dx](https://tex.z-dn.net/?f=W%20%3D%20%5Cint%5E%7B1.6%7D_0%20%288x-5x%5E2%29dx)
![W = \Big[\frac{8x^2}{2}-\frac{5x^3}{3}\Big]^{1.6}_0](https://tex.z-dn.net/?f=W%20%3D%20%5CBig%5B%5Cfrac%7B8x%5E2%7D%7B2%7D-%5Cfrac%7B5x%5E3%7D%7B3%7D%5CBig%5D%5E%7B1.6%7D_0)
![W = \frac{8(1.6^2)}{2}-\frac{5(1.6^3)}{3}](https://tex.z-dn.net/?f=W%20%3D%20%5Cfrac%7B8%281.6%5E2%29%7D%7B2%7D-%5Cfrac%7B5%281.6%5E3%29%7D%7B3%7D)
![W = 3.44J](https://tex.z-dn.net/?f=W%20%3D%203.44J)
PART C) At the moment when the work reaches zero, we will simply match the integral previously found to zero value so
![w = \frac{8x^2}{2}-\frac{5x^3}{3}](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B8x%5E2%7D%7B2%7D-%5Cfrac%7B5x%5E3%7D%7B3%7D)
![\frac{8x^2}{2}=\frac{5x^3}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B8x%5E2%7D%7B2%7D%3D%5Cfrac%7B5x%5E3%7D%7B3%7D)
![24=10x](https://tex.z-dn.net/?f=24%3D10x)
![x = 2.4m](https://tex.z-dn.net/?f=x%20%3D%202.4m)
PART D ) If the work is zero in position 2.4, do not open movement, as the distance to travel will also be 0. The body will be at rest again 2.4m from its initial position.
Answer:
![-10 m/s](https://tex.z-dn.net/?f=-10%20m%2Fs)
Explanation:
When two cars collide then the momentum of two cars will remains conserved
- Mass of two cars = 100 kg
-
Speed of car B = - 10 m/s
-
After collision the speed of car B = +8 m/s
By momentum conservation equation
![m1v1i+m2v2i=m1v1f + m2v2f](https://tex.z-dn.net/?f=m1v1i%2Bm2v2i%3Dm1v1f%20%2B%20m2v2f)
![(100)(8)+(100)(-10)=(100v)+(100)(8)\\ v=-10 m/s](https://tex.z-dn.net/?f=%28100%29%288%29%2B%28100%29%28-10%29%3D%28100v%29%2B%28100%29%288%29%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20v%3D-10%20m%2Fs)