Sau-Lan has a mass of 47 kg. She rides the up escalator at Ocean Park in Hong Kong. This is the world's longest escalator, with a length of 227 m and an average inclination of 31°. How much work does the escalator do on Sau-Lan?

Well, I hate to burst your bubble, but escalators are not typically known for their work ethic. If anything, they usually just make people lazier. But I’m here to help, so let’s calculate this "work" regardless.

To find the work done by the escalator, we can use the formula:

Work = force x distance x cosθ

θ being the angle of inclination. Now, since Sau-Lan is riding the escalator, the force she exerts is mainly perpendicular to the direction of motion. Therefore, we can assume the escalator's force is doing all the work.

The force can be calculated by multiplying Sau-Lan's mass (47 kg) by the gravitational acceleration (9.8 m/s²). So the force is:

Force = Mass x Acceleration
= 47 kg x 9.8 m/s²
= 461.6 N

Now we can plug in the values into the work formula:

Work = Force x Distance x cosθ
= 461.6 N x 227 m x cos(31°)

Welp, I guess it’s time to do some math. Give me a moment.

*sounds of calculators clacking*

Ah, here it is! The work done by the escalator on Sau-Lan is approximately equal to 33,958.5 Joules.

So, the world's longest escalator does about 33,958.5 Joules of work on Sau-Lan. Keep in mind, though, that she probably isn't too grateful for all that extra effort she's putting in to not move as much.

To calculate the work done by the escalator on Sau-Lan, we need to find the vertical component of the force exerted by the escalator and multiply it by the distance traveled.

1. First, let's calculate the vertical component of Sau-Lan's weight. This can be found by multiplying her mass by the acceleration due to gravity:
Weight = mass * acceleration due to gravity
= 47 kg * 9.8 m/s^2
= 461.6 N

2. Next, we need to find the vertical component of the force due to gravity. This can be found by multiplying the weight by the sin of the angle of inclination:
Vertical Force due to gravity = Weight * sin(angle of inclination)
= 461.6 N * sin(31°)
= 233.7 N

3. Now, we can calculate the work done by the escalator. The work done is equal to the force multiplied by the distance traveled:
Work = Force * Distance
= 233.7 N * 227 m
= 53,051.9 J (Joules)

Therefore, the escalator does approximately 53,051.9 Joules of work on Sau-Lan.

To calculate the work done by the escalator on Sau-Lan, we need to use the formula:

Work = Force × Distance × cos(θ)

Here, Force refers to the component of the force parallel to the direction of motion, Distance is the length of the escalator, and θ is the angle of inclination.

First, let's find the component of Sau-Lan's weight parallel to the direction of motion. This can be calculated using:

Force = Mass × Acceleration due to gravity

Since acceleration due to gravity is approximately 9.8 m/s^2, we have:

Force = 47 kg × 9.8 m/s^2

Next, we need to find the distance. Given that the length of the escalator is 227 m, the distance traveled by Sau-Lan while riding the escalator is 227 m.

Finally, we need to calculate the angle of inclination in radians. Since the given angle is in degrees, we convert it to radians using the formula:

θ (in radians) = θ (in degrees) × π / 180

Substituting the values into the formula, we have:

θ (in radians) = 31° × π / 180

Now we can calculate the work done by the escalator:

Work = (Force) × (Distance) × cos(θ)

Plug in the values calculated earlier, and we can find the work done by the escalator on Sau-Lan.

M*g*227*sin 31 = 53,850 Joules

227sin31 is the elevation change.