Answer :
To solve this problem, let's break it down into steps:
1. Understand the Energy Requirement:
- The building uses 11,000 kilowatt-hours (kWh) of energy each day. We also know this is equal to about [tex]\(4.0 \times 10^{10}\)[/tex] Joules.
2. Energy Provided by Each Rider:
- Each student riding an exercise bike provides an average power of 100 Watts. Remember, 1 Watt (W) is equivalent to 1 Joule per second.
- Each rider works an 8-hour shift. To find out how much energy one rider provides in one shift, we need to convert the time to seconds because power is in Watts (Joules per second).
- There are 3600 seconds in an hour, so in 8 hours, there are [tex]\(8 \times 3600 = 28,800\)[/tex] seconds.
3. Calculate Energy by One Rider:
- The energy provided by one rider in one shift is:
[tex]\[
\text{Energy per rider} = \text{Power} \times \text{Time} = 100 \, \text{W} \times 28,800 \, \text{s} = 2,880,000 \, \text{Joules}
\][/tex]
4. Determine the Number of Riders Needed:
- We need to find out how many riders are required to meet the total energy need of [tex]\(4.0 \times 10^{10}\)[/tex] Joules.
- The number of riders required can be calculated using the formula:
[tex]\[
\text{Number of riders} = \frac{\text{Total energy needed}}{\text{Energy per rider}}
\][/tex]
[tex]\[
= \frac{4.0 \times 10^{10} \, \text{Joules}}{2,880,000 \, \text{Joules per rider}}
\][/tex]
5. Final Calculation:
- Calculating this gives approximately 13,888.89 riders.
So, around 13,889 riders are needed to supply the 11,000 kWh of energy required by the building for one day.
1. Understand the Energy Requirement:
- The building uses 11,000 kilowatt-hours (kWh) of energy each day. We also know this is equal to about [tex]\(4.0 \times 10^{10}\)[/tex] Joules.
2. Energy Provided by Each Rider:
- Each student riding an exercise bike provides an average power of 100 Watts. Remember, 1 Watt (W) is equivalent to 1 Joule per second.
- Each rider works an 8-hour shift. To find out how much energy one rider provides in one shift, we need to convert the time to seconds because power is in Watts (Joules per second).
- There are 3600 seconds in an hour, so in 8 hours, there are [tex]\(8 \times 3600 = 28,800\)[/tex] seconds.
3. Calculate Energy by One Rider:
- The energy provided by one rider in one shift is:
[tex]\[
\text{Energy per rider} = \text{Power} \times \text{Time} = 100 \, \text{W} \times 28,800 \, \text{s} = 2,880,000 \, \text{Joules}
\][/tex]
4. Determine the Number of Riders Needed:
- We need to find out how many riders are required to meet the total energy need of [tex]\(4.0 \times 10^{10}\)[/tex] Joules.
- The number of riders required can be calculated using the formula:
[tex]\[
\text{Number of riders} = \frac{\text{Total energy needed}}{\text{Energy per rider}}
\][/tex]
[tex]\[
= \frac{4.0 \times 10^{10} \, \text{Joules}}{2,880,000 \, \text{Joules per rider}}
\][/tex]
5. Final Calculation:
- Calculating this gives approximately 13,888.89 riders.
So, around 13,889 riders are needed to supply the 11,000 kWh of energy required by the building for one day.
