A trough is 8 meters long, 3 meters wide, and 5 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 5 meters, and base, on top, of length 3 meters). The trough is full of water (density ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use as the acceleration due to gravity.)
I keep getting 122500 as an answer and my online homework keeps saying that it's wrong. I've tried other ways but it's still incorrect
To find the amount of work required to empty the trough, we need to calculate the gravitational potential energy of the water in the trough.
The formula for gravitational potential energy is given by:
Potential Energy = mass x acceleration due to gravity x height
Let's first calculate the mass of the water in the trough.
The volume of the trough can be found by multiplying its length, width, and depth:
Volume = length x width x depth
Volume = 8 m x 3 m x 5 m
Volume = 120 cubic meters
Since water has a density of 1000 kilograms per cubic meter, we can calculate the mass of the water:
Mass = density x volume
Mass = 1000 kg/m^3 x 120 m^3
Mass = 120,000 kg
Now we can calculate the amount of work required to pump the water out of the trough and over the top.
Work = Potential Energy = mass x acceleration due to gravity x height
Given:
Mass = 120,000 kg
Acceleration due to gravity = 9.8 m/s^2
Height = 5 m
Work = 120,000 kg x 9.8 m/s^2 x 5 m
Work = 5,880,000 Joules
Therefore, the amount of work required to empty the trough by pumping the water over the top is 5,880,000 Joules.
To find the amount of work required to empty the trough, we need to calculate the potential energy of the water in the trough and then convert it into work.
Step 1: Calculate the volume of the trough.
The trough has a length of 8 meters, a width of 3 meters, and a depth of 5 meters. The volume of a rectangular prism, which the trough represents, is given by V = length x width x height. Therefore, the volume of the trough is V = 8m x 3m x 5m = 120 cubic meters.
Step 2: Calculate the mass of the water in the trough.
The density of water is usually given as 1000 kg/m^3. Since the density is mass/volume, we can rearrange the formula to find the mass: mass = density x volume. Therefore, the mass of water in the trough is mass = 1000 kg/m^3 x 120 m^3 = 120,000 kg.
Step 3: Calculate the potential energy of the water.
The potential energy of an object depends on its height, mass, and acceleration due to gravity. The formula for potential energy is PE = mass x acceleration due to gravity x height. In this case, the height is 5 meters, the mass is 120,000 kg, and the acceleration due to gravity (g) is 9.8 m/s^2. Thus, the potential energy of the water in the trough is PE = 120,000 kg x 9.8 m/s^2 x 5 m = 5,880,000 joules.
Step 4: Convert potential energy to work.
The potential energy is the amount of energy needed to move the water from its current position to a higher point. To convert this potential energy into work, we use the formula for work: work = force x distance. In this case, the force is the weight of the water, which is equal to the mass times the acceleration due to gravity (force = mass x acceleration due to gravity). The distance is the height of the trough, which is 5 meters. Thus, the work required to empty the trough is work = force x distance = mass x acceleration due to gravity x distance = 120,000 kg x 9.8 m/s^2 x 5 m = 5,880,000 joules.
Therefore, the amount of work required to empty the trough by pumping the water over the top is 5,880,000 joules.
need rules of physics here.
volume of water if trough is full
= (1/2)(3)(5)(8)
= 60 cubic metres
from here on it is physics