A total of 100000 kg of water per second flows over a waterfall 30 m high. If half of the power this flow represents could be converted into electricity, how many 100 watt lightbulbs could be supplied?
0.5mgh/t=0.5•10⁵•9.8•30=1.47•10⁷ W
N= 1.47•10⁷/100=1.47•10⁵
5.5
To determine how many 100-watt lightbulbs could be powered, we need to calculate the power of the flowing water.
The power of the flowing water can be calculated using the formula: power = mass flow rate * acceleration due to gravity * height
Given:
- Mass flow rate of water (m_dot) = 100000 kg/s
- Height of the waterfall (h) = 30 m
Let's calculate the power of the flowing water:
power = m_dot * g * h
where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
power = 100000 kg/s * 9.8 m/s^2 * 30 m
power = 29400000 Watts
Since we can convert half of this power into electricity:
power_converted = 29400000 Watts / 2
power_converted = 14700000 Watts
Now, let's calculate the number of 100-watt lightbulbs that can be powered:
number_of_lightbulbs = power_converted / 100 Watts
number_of_lightbulbs = 14700000 Watts / 100 Watts
number_of_lightbulbs = 147000
Therefore, the flowing water could power approximately 147,000 100-watt lightbulbs.
To find out how many lightbulbs can be supplied by the power generated from the flowing water, we need to determine the power of the flowing water and then divide it by the power consumption of a single lightbulb.
First, let's calculate the power of the flowing water:
Power (P) = Mass flow rate (m) x Gravity (g) x Height (h)
Given:
- Mass flow rate (m) = 100,000 kg/s
- Gravity (g) = 9.8 m/s²
- Height (h) = 30 m
Plugging in these values into the power formula:
P = 100,000 kg/s x 9.8 m/s² x 30 m
P = 29,400,000 W
Now, since we're converting only half of the power into electricity, we need to calculate half of the obtained power:
Converted Power = 0.5 x Power
Converted Power = 0.5 x 29,400,000 W
Converted Power = 14,700,000 W
Finally, we can find out how many 100-watt lightbulbs this converted power can supply:
Number of Lightbulbs = Converted Power / Power Consumption per Lightbulb
Number of Lightbulbs = 14,700,000 W / 100 W
Number of Lightbulbs = 147,000
Therefore, the flowing water from the waterfall could supply electricity to approximately 147,000 100-watt lightbulbs.