Squaw Valley ski area in California claims that its lifts can move 48700 people per hour. If the average lift carries people about 185 m (vertically) higher, estimate the maximum total power needed. (Assume an average mass per person of 70 kg.)
Power is the rate of doing work.
The work associated with taking an average person to the top is M g H = 70*9.8*185 = ___ Joules.
Multiply that by the number of people carried per SECOND. The answer will be in Watts.
To estimate the maximum total power needed, we need to find the work done by the lifts per hour.
The work done by a lift can be calculated using the formula:
Work = Force x Distance
Force can be calculated using the formula:
Force = mass x acceleration
Acceleration is the change in velocity over time. However, since the lift moves at a constant velocity, acceleration is zero. Therefore, the force can be simplified to:
Force = mass x 0 = 0
Hence, the lift does not exert any force. Instead, the work done is against gravity. The work done against gravity can be calculated using the formula:
Work = mass x gravity x height
Here, the height is the vertical distance moved by the lift, which is given as 185 m.
Substituting the values, we have:
Work = 70 kg x 9.8 m/s^2 x 185 m = 126,630 J
The maximum total power needed can be calculated using the formula:
Power = Work / Time
Since the lifts can move 48,700 people per hour, we can assume that each person takes 1 hour to reach the desired height.
Substituting the values, we have:
Power = 126,630 J / 1 hour = 126,630 J/hour
Hence, the estimated maximum total power needed is 126,630 J/hour.
To estimate the maximum total power needed for Squaw Valley ski area lifts, we can use the following steps:
Step 1: Calculate the total mass being lifted per hour.
To do this, we need to find the number of people being carried per hour. The ski area claims to be able to move 48700 people per hour.
Total mass = Number of people * Average mass per person
Total mass = 48700 * 70 kg
Step 2: Calculate the total work done to lift the mass.
The work done is equal to the change in potential energy, given by the formula:
Work = Force * Distance
In this case, the force is equal to the weight of the lifted mass. The distance is the vertical rise, which is 185 m.
Work = Mass * Gravity * Distance
Work = Total mass * 9.8 m/s^2 * 185 m
Step 3: Calculate the power required per hour.
Power is the rate at which work is done, given by the formula:
Power = Work / Time
In this case, the time is one hour.
Power = Work / 3600 seconds
Step 4: Convert the power to kilowatts.
To convert the power from watts to kilowatts, divide by 1000.
Now we can put all the values together and calculate the maximum total power needed:
Total mass = 48700 * 70 kg = 3,409,000 kg
Work = 3,409,000 kg * 9.8 m/s^2 * 185 m = 6,013,858,000 J
Power = 6,013,858,000 J / 3600 s = 1,670,516.1 W
Power (in kilowatts) = 1,670,516.1 W / 1000 = 1670.5 kW
So, the estimated maximum total power needed for Squaw Valley ski area lifts is approximately 1670.5 kilowatts.