Karen has a mass of 62.60 kg and she rides the up escalator at Woodley Park Station of the Washington D.C. Metro. Karen rode a distance of 62 m, the longest escalator in the free world. How much work did the escalator do on Karen if it has an inclination of 35°?
Work = M*g*L*sin235
L = 62 m
L sin35 is the elevation gain
To calculate the work done by the escalator on Karen, we need to use the gravitational force formula and the formula for calculating work.
First, let's calculate the gravitational force acting on Karen. The formula for gravitational force is given by:
F = m * g
Where:
F = gravitational force
m = mass of the object (Karen)
g = acceleration due to gravity
In this case, the mass of Karen is given as 62.60 kg. The acceleration due to gravity on Earth is 9.8 m/s^2. Plugging in these values, we get:
F = 62.60 kg * 9.8 m/s^2 = 612.28 N
Next, we need to calculate the component of the gravitational force parallel to the direction of motion of the escalator. This component can be found using trigonometry.
The formula to calculate the parallel component of the force is:
F_parallel = F * sin(θ)
Where:
F_parallel = component of the force parallel to the direction of motion
F = gravitational force
θ = angle of inclination of the escalator
In this case, the angle of inclination is given as 35°. Plugging in the values, we get:
F_parallel = 612.28 N * sin(35°) = 350.72 N
Finally, we can calculate the work done by the escalator using the formula:
Work = force * distance
In this case, the distance ridden by Karen is given as 62 m. Plugging in the values, we get:
Work = 350.72 N * 62 m = 21,744.64 J (Joules)
Therefore, the escalator did 21,744.64 Joules of work on Karen.