Flag question Consider the pressure and force acting on the
dam retaining a reservoir of water. Suppose the
dam is 500-m wide
and the water is 80.0-m
deep at the dam, as illustrated below. What is
the average pressure on the dam due to the
water?​

P = density (p) * g * h

P = 1000  kg/m^3 * 9.8 m/s^2 * 40 m = 392,000 N/m^2

since kg m / s^2 = Newtons

The average pressure is 1/2 (pressure at 0m +  pressure 80 m) for liquid of uniform density

We can conclude 2.3x10^7 J was converted to thermal energy

Explanation:

Energy Conservation

According to the law of conservation of energy, the total energy of an isolated system must be constant. If some kind of energy is 'lost', we know it was transformed into another type.

Let's check the conditions of the problem. The ride vertically drops a distance of 71.6 m starting from rest, and at the bottom of the drop, its speed is 10 m/s. Knowing the mass of the cart plus passengers is 3.5X10^4 kg, we compute the total energy at the top of the drop.

Where E is the total energy (which must be conserved) at the top of the drop, U is the gravitational potential energy and K is the kinetic energy. We use the equations for each:

At the top, the speed is 0, thus

Now we compute the 'total' energy at the bottom (quoted because we know there is some mechanical energy loss in the drop)

This time h'=0 and v=10 m/s, thus

The mechanical energy at the top and the bottom are not the same, thus we can know part of it was converted to heat or thermal energy. We compute the difference

We can conclude 2.3x10^7 J was converted to thermal energy