Anyone can help me with these questions:
1. BC Hydro charges $5.91 per kWh. How long does it take a 100 W light bulb to use up $1.00 of energy? (answer = 1.7h)
2. A small bag of chips contains 230 Calories (1000 calories = 1 calorie = 4.19 kJ). To what max. height could a 70 kg person climb with this amount of energy?
Thanks :)
P=100 W =0.1 kW
0.1•t kWh → $1
1 kWh → $5.91
t=1/0.1•5.91 =1.7 h
2.
1000 calories = 1 kilocalorie = 4.19 kJ
mgH=70•9.8•H = 230 C = 963 J
H= 963/70•9.8 =1.4 m
Of course! I'd be happy to help you with these questions and explain how to find the answers.
1. To determine how long it takes a 100 W light bulb to use up $1.00 of energy, you need to calculate the amount of energy consumed by the light bulb in $1.00.
The unit of energy consumed by the light bulb is kilowatt-hours (kWh). We can calculate the amount of energy consumed by the light bulb in kWh by dividing the power rating of the bulb by 1000 (since 1 kW = 1000 W). So in this case, the power of the light bulb is 100 W, which is equal to 0.1 kW.
To calculate the energy consumed by the light bulb in kWh, we divide $1.00 by the cost per kWh. In this case, the cost is $5.91 per kWh. So,
Energy consumed = $1.00 / $5.91 per kWh
Now, to find how long it takes for the light bulb to consume this amount of energy, we divide the energy consumed by the power rating of the light bulb (in kW).
Time = Energy consumed / Power rating
Plugging in the values from above, we have:
Time = ($1.00 / $5.91 per kWh) / 0.1 kW
Simplifying this expression gives us:
Time = 10.170h
Rounding this to the nearest hundredth, we get the answer as approximately 1.7 hours.
So, it takes about 1.7 hours for a 100 W light bulb to use up $1.00 of energy from BC Hydro.
2. To find the maximum height a 70 kg person could climb using the energy from a bag of chips, we need to convert the energy value from Calories to joules.
As given, 1000 calories = 1 calorie = 4.19 kJ. So, to convert 230 Calories to joules, we multiply it by the conversion factor:
Energy in joules = 230 Calories * 4.19 kJ/Calorie
Now we have the total energy available in joules. To calculate the maximum height the person can climb, we use the concept of potential energy.
Potential energy (PE) = mass * gravitational acceleration * height
Here, the mass is 70 kg and the gravitational acceleration is approximately 9.8 m/s^2 (assuming Earth's gravity). We can rearrange the equation to solve for height:
Height = PE / (mass * gravitational acceleration)
Now, we can substitute the energy in joules (which is the potential energy) into the equation:
Height = (Energy in joules) / (mass * gravitational acceleration)
Plugging in the values:
Height = (230 Calories * 4.19 kJ/Calorie) / (70 kg * 9.8 m/s^2)
Simplifying this expression gives us:
Height ≈ 12.96 meters
So, with the energy from the bag of chips, a 70 kg person could climb to a maximum height of approximately 12.96 meters.
I hope this helps! Let me know if you have any further questions.