Question

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is1000 kg/m3.)Show how to approximate the required work by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter xi* as xi.)lim n ? ?

Answer 1

Answer:

Workdone = 2450Joules

Step-by-step explanation:

Let the top of the aquarium be at height 0.

Let the bottom of the aquarium be at height 1

F = mg = 2p◇x × g

F= 2000◇x × 9.8

F = 19600◇x

Workdone = 19600xdx

Total workdone = Integral (limits 0.5 -0)19600×dx

Total work = [9800x^2]^0.5

Total work= 9800× 0.5^2 = 2450 Joules

Answer 2

In this exercise we have to use our working knowledge to calculate the height of the tank, so we have:

$W = 2450Joules$

From the following information given in the statement, we can calculate the work as:

• Let the top of the aquarium be at height 0.

• Let the bottom of the aquarium be at height 1

So, the force is equal to:

$F = mg = 2px * g\\F= 2000x * 9.8\\F = 19600x$

The total work done will be:

$W=\int\limits^{0.5}_0 {19600x} \, dx= 2450 Joules$

See more about work at brainly.com/question/1374468