a trough is 8 meters long, 2.5 meters wide, & 3 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isosceles triangle (with height 3 meters, and base, on top, of length 2.5 meters). The trough is full of water (density 1000 kg÷ m3). Find the amount of work in joules required to empty the trough by pumping the water over the top.) (Note: Use g=9.8 m÷a2 as the acceleration due to gravity.)
To find the amount of work required to empty the trough by pumping the water over the top, we need to calculate the gravitational potential energy of the water in the trough.
The volume of the trough can be calculated by multiplying its length, width, and depth:
Volume = Length x Width x Depth
Volume = 8 m x 2.5 m x 3 m
Volume = 60 cubic meters
The mass of the water can be found using its density:
Mass = Density x Volume
Mass = 1000 kg/m^3 x 60 m^3
Mass = 60000 kg
The height from which the water is lifted is the total depth of the trough, which is 3 meters.
Gravitational Potential Energy = Mass x Gravity x Height
Gravitational Potential Energy = 60000 kg x 9.8 m/s^2 x 3 m
Gravitational Potential Energy = 1764000 Joules
Therefore, the amount of work required to empty the trough by pumping the water over the top is 1,764,000 Joules.
To find the amount of work required to empty the trough by pumping the water over the top, we need to calculate the gravitational potential energy of the water in the trough.
The gravitational potential energy (PE) of an object is given by the equation:
PE = m * g * h
Where:
m is the mass of the object
g is the acceleration due to gravity (9.8 m/s^2)
h is the height above the reference point
To find the mass of the water in the trough, we first need to calculate the volume of the water.
The volume of the trough is given by the formula:
V = l * w * h
Where:
l is the length
w is the width
h is the depth
Given:
Length (l) = 8 meters
Width (w) = 2.5 meters
Depth (h) = 3 meters
V = 8 * 2.5 * 3
V = 60 cubic meters
Since the trough is already full of water, the volume of the water is equal to the volume of the trough.
Now, we can calculate the mass of the water using the density of water:
Density of water (ρ) = 1000 kg/m^3
m = ρ * V
m = 1000 * 60
m = 60000 kg
Now that we have the mass of the water, we can calculate the potential energy using the formula mentioned earlier.
PE = m * g * h
PE = 60000 * 9.8 * 3
PE = 1764000 joules
Therefore, the amount of work required to empty the trough by pumping the water over the top is 1,764,000 joules.
the weight of water is 1/2 * 3 * 2.5 * 8 * 1000 * 9.8 = 29400 N
The center of mass of the water is at a depth of 1 meter
so, the work required is 29400N * 1m = 29400 J