Answer:
W = 1.06 MJ
Explanation:
- We will use differential calculus to solve this problem.
- Make a differential volume of water in the tank with thickness dx. We see as we traverse up or down the differential volume of water the side length is always constant, hence, its always 8.
- As for the width of the part w we see that it varies as we move up and down the differential element. We will draw a rectangle whose base axis is x and vertical axis is y. we will find the equation of the slant line that comes out to be y = 0.5*x. And the width spans towards both of the sides its going to be 2*y = x.
- Now develop and expression of Force required:
F = p*V*g
F = 1000*(2*0.5*x*8*dx)*g
F = 78480*x*dx
- Now, the work done is given by:
W = F.s
- Where, s is the distance from top of hose to the differential volume:
s = (5 - x)
- We have the work as follows:
dW = 78400*x*(5-x)dx
- Now integrate the following express from 0 to 3 till the tank is empty:
W = 78400*(2.5*x^2 - (1/3)*x^3)
W = 78400*(2.5*3^2 - (1/3)*3^3)
W = 78400*13.5 = 1058400 J
Answer:
Total momentum, p = 21.24 kg-m/s
Explanation:
Given that,
Mass of first piece, 
Mass of the second piece, 
Speed of the first piece,
(along x axis)
Speed of the second piece,
(along y axis)
To find,
The total momentum of the two pieces.
Solve,
The total momentum of two pieces is equal to the sum of momentum along x axis and along y axis.






The net momentum is given by :


p = 21.24 kg-m/s
Therefore, the total momentum of the two pieces is 21.24 kg-m/s.
Explanation:
The height of the rise of liquid with capillary tube is given by the formula as follows :

Where
r is radius
It is clear that the height of the rise of liquid is inversely proportional to the radius of the capillary tube.
If the radius of the capillary tube is doubled, it means the height of rise of liquid with capillary tube become half.
Answer:
The maximum speed is 21.39 m/s.
Explanation:
Given;
radius of the flat curve, r₁ = 150 m
maximum speed,
= 32.5 m/s
The maximum acceleration on the unbanked curve is calculated as;

the radius of the second flat curve, r₂ = 65.0 m
the maximum speed this unbanked curve should be rated is calculated as;

Therefore, the maximum speed is 21.39 m/s.