An elevator lifts 5 passengers 30 meters in 24 seconds. The power is 15,000w. What is the total weight of the elevator and passengers?
P = Mg*h/t = Mg * 30/24 = 15,000
Mg = 12,000 N. = Total Wt.
To find the total weight of the elevator and passengers, we need to calculate the force exerted by the elevator.
First, let's calculate the work done by the elevator using the formula:
Work = force × distance
Given that the elevator lifts 5 passengers by 30 meters, the work done by the elevator can be calculated as:
Work = force × 30 meters
Next, we can calculate the power using the formula:
Power = work / time
Given that the power is 15,000 watts and the time is 24 seconds, we can rewrite the formula as:
15,000 watts = Work / 24 seconds
Now, let's substitute the work value from the first equation into the second equation:
15,000 watts = (force × 30 meters) / 24 seconds
Next, we can rearrange the equation to solve for force:
force = (15,000 watts × 24 seconds) / 30 meters
Now, we can calculate the force exerted by the elevator:
force = (15,000 watts × 24 seconds) / 30 meters
= 12,000,000 joules / 30 meters
= 400,000 newtons
Finally, to find the total weight of the elevator and passengers, we can convert the force to kilograms using the Earth's gravitational acceleration of 9.8 m/s²:
Weight = force / acceleration
Weight = 400,000 newtons / 9.8 m/s²
≈ 40,816 kilograms
Therefore, the total weight of the elevator and passengers is approximately 40,816 kilograms.
To find the total weight of the elevator and passengers, we need to find the force exerted by the elevator.
First, let's calculate the work done by the elevator using the formula:
Work = Force x Distance
Given:
- The distance lifted by the elevator is 30 meters.
- The time taken is 24 seconds.
- The power is 15,000 watts.
Since power is defined as the rate at which work is done, we can rearrange the equation to solve for force:
Power = Work / Time
Therefore, Work = Power x Time
Substituting the given values:
Work = 15,000 watts x 24 seconds
Next, we can calculate force using the equation:
Force = Work / Distance
Substituting the values:
Force = (15,000 watts x 24 seconds) / 30 meters
The force calculated here represents the net force exerted by the elevator to lift the passengers. However, the weight is the force experienced due to gravity exerted by the elevator and passengers.
Thus, we can say:
Weight = Force
Hence, the total weight of the elevator and passengers is equal to the force calculated earlier.