Answer:
4.41 × 10¹² J, 2.72 × 10³ m³, 0.907 × 10 ⁻³ m
Explanation:
Gravitational potential energy = mgh
where m is mass in kg, g is acceleration due to gravity in m/s², and h is the distance from the base of the dam.
mass of the surface water = density of water × volume of water × 1 m = 1000 kg / m³ × 3.0 × 10⁶ m² × 1 m = 3 × 10⁹ kg
Gravitational potential energy = 3 × 10⁹ kg × 9.81 m/s² × 150 m = 4.41 × 10¹² J
b)what volume of water must pass through the dam to produce 1000 kw-hrs
1 000 kw-hr = 3.6 × 10 ⁹ J
the dam has mechanical energy conversion of 90% to electrical energy
Gravitational potential energy needed = 3.6 × 10 ⁹ J / 0.9 = 4 × 10⁹ J
mass of water needed = Energy required / g h = 4 × 10⁹ J / (9.81 m/s² × 150 m) = 2.718 × 10 ⁶ kg
density = mass / volume
volume = mass / density = 2.718 × 10 ⁶ kg / (1000 kg/ m³) = 2.72 × 10³ m³
the distance the level of the water in the lake fell = volume / area = 2.72 × 10³ m³ / (3.0×10⁶ m²) = 0.907 × 10 ⁻³ m
Answer:
2188 years
Explanation:
given,
see level rising at the rate = 3.2 mm/yr
height of the sea level to rise = 7 m
time it will take rise 7 m = ?
we know,
1 m = 1000 mm
1 mm = 0.001 m
rate of increase of rate = 0.0032 m/year
time taken to rise = 
= 2187.5 years
Now, time taken by the sea level to rise 7 m is equal to 2188 years.
Using the given formula with v0=56 ft/s and h=40 ft
h = -16t2 + v0t
40 = -16t2 + 56t
16t2 - 56t + 40 = 0
Solving the quadratic equation:
t= (-b+/-(b^2-4ac)^1/2)/2a = (56+/-((-56)^2-4*16*40)^1/2)/2*16 = (56 +/- 24) / 32
We have two possible solutions
t1 = (56+24)/32 = 2.5
t2 = (56-24)/32 = 1
So initially the ball reach a height of 40 ft in 1 second.
Dab
10. <span>A block with mass m = 6.2 kg is attached to two springs with spring constants kleft = 31.0 N/m and kright = 49.0 N/m. The block is pulled a distance x = 0.2 m to the left of its equilibrium position and released from rest
</span>
<u>Answer</u>
27.7
<u>Explanation</u>
The ball was hit at an angle of 30°, with the horizontal at a speed of 10 m/s. We have to find the horizontal component of speed.
cosx = adjacent/hypotenuse
cos 30 = adjacent / 10
adjacent = 10 cos30
= 8.66 m/s ⇒ This is the horizontal speed.
Now find the horizontal distance.
Distance = speed × time
= 8.66 × 3.2
= 27.71
Answer to the nearest tenth = 27.7
