A chair lift carries people of average mass 75kg to a height of 450m above the starting point. Calculate a) the work done by the chair lift to move one person through 450m. b) the power expended to carry 60 people every 5 minutes.
a) M*g*H joules per (average) person
b) 60*M*g*H/300 s
To calculate the work done by the chair lift, we can use the formula:
Work = Force * Distance * cos(θ)
Where:
- Force is the weight of the person, given by the formula: Force = mass * gravity
- Distance is the height the person is lifted, given as 450m
- θ is the angle between the direction of the force and the direction of motion. In this case, θ is 0° because the force is in the same direction as the motion.
a) Calculate the work done by the chair lift to move one person through 450m:
- Mass of one person = 75kg
- Acceleration due to gravity = 9.8m/s²
Step 1: Calculate the force:
Force = mass * gravity
Force = 75kg * 9.8m/s²
Step 2: Calculate the work:
Work = Force * Distance * cos(θ)
Work = (75kg * 9.8m/s²) * 450m * cos(0°)
Since cos(0°) = 1, the equation simplifies to:
Work = (75kg * 9.8m/s²) * 450m
Calculate the result.
b) To calculate the power expended to carry 60 people every 5 minutes, we need to determine the work done and divide it by the time taken:
Step 1: Calculate the work done by one person using the formula from part a:
Work per person = (75kg * 9.8m/s²) * 450m
Step 2: Calculate the total work done for 60 people:
Total work = Work per person * Number of people
Step 3: Convert the time from minutes to seconds:
Time = 5 minutes = 5 * 60 seconds
Step 4: Calculate the power:
Power = Total work / Time
Calculate the result.