The minimum required motor power for cleaning the torch of the Statue of Liberty
What is the minimum required motor power for the torch-cleaning robot to ascend to the tip of the torch in 30 seconds?
Answer:
The minimum required motor power is 3,038 Watts.Explanation:
The torch at the top of the Statue of Liberty needs cleaning! Our torch-cleaning robot has a mass of 100kg and needs to ascend vertically from ground-level to the tip of the torch in 30 seconds.
In order to calculate the minimum required motor power, we can use the following steps:
Step 1: Calculate the final velocity of the robot:
The distance from ground-level to the tip of the torch is 92.99 m. Using the kinematic equation Vf² = 2as, where a is the acceleration (9.8 m/s²) and s is the displacement (92.99 m), we find that the final velocity of the robot is 42.64 m/s.
Step 2: Calculate the work done by the robot:
Using the formula W = mgh, where m is the mass of the robot (100 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the torch (92.99 m), we determine that the work done is 91,454.2 Joules.
Step 3: Calculate the power required:
Power is equal to work done divided by the time taken. With a work done of 91,454.2 J and a time taken of 30 seconds, the power required is 3,048.47 W.
Step 4: Understand the relationship between power input and output:
Since the rate of climb has no drag or friction, the power output must match the power input. The minimum required motor power is indeed 3,038 Watts.
Therefore, to clean the torch of the Statue of Liberty, the torch-cleaning robot needs a minimum motor power of 3,038 Watts to ascend vertically to the tip of the torch in 30 seconds.