Hi guys. I have three problems that I'm not quite sure how to approach. They revolve around the idea of work and force.
1. The first problem is this:
Consider a trough 15 m long and 11 m high with a triangular cross section that is 5 m wide at the top. The trough contains water (1000 kg/m^3) to a depth of 8 m.
A. Calculate the work required to pump the water to the top of the trough.
B. Calculate the force of the water on the triangular end of the trough.
For the work, this is what I'm thinking the set-up of the integral is:
1000(9.8) * integral of (y * (11-y)) dy, integrating from 0 to 8.
For the force, this is what I'm thinking the set-up for the integral is:
1000(5/11) * integral of (y * (11-y)) dy, integrating from 0 to 8.
Am I even remotely close here, or am I completely off? I feel like the work problem is okay, but the force on the side makes me feel lost and unsure of myself.
2. For problem 2, it asks to consider a trough 12 m long with a semicircular cross-section with a radius of 4 m. The trough contains water to a depth of 3 m. The problems are the same, where it asks me to find the work required to pump the water to the top of the trough and the force of the water on the semicircular end of the trough.
For the work, here is my idea:
1000(9.8)(0.5(pi)) * integral of (x * (4-x)^2), integrating from 0 to 3.
For the force, I'm very lost. I want to say there is the use of the Pythagorean Theorem, but other then that, I have no idea of where to even begin outside of knowing that you'd be integrating from 0 to 3.
3. For the last problem, it asks to consider a trough 20 m long and 6 m high with a trapezoidal cross section 5 m wide at the base and 8 m wide at the top. The trough contains water to a depth of 4 m. The problems ask for the work required to pump the water to the top of the trough and the force of the water on the trapezoidal end of the trough. My teacher gave us a boost on the work set-up.
For work, this is what I think it is:
1000(9.8) * integral of (4-x) * (5 + 0.5x) dx, integrating from 0 to 4.
For force, though, I am lost, outside of knowing that I should be integrating from 0 to 4.
Sorry guys. I know that my formatting is very "ugly", but any help is greatly appreciated!