Question

5. Juan has a mass of 57.2 kg. He walks up a 4.2 m staircase in 8.76 seconds. Calculate the work he
did.

Answer 1

Work is done against gravity, and it's stored as gravitational potential energy
\[Work = m\times g\times h\]
m= mass
g= acceleration due to gravity
h= height
m=57.2 kg
g= 9.8 m/s^2
h=4.2 m
\[Work=57.2 \times 9.8 \times 4.2 Joules\]
I think you can solve now.

Answer 2

Work is force times distance and the cosine of the angle between the force and direction of the distance. So if the angle between the distance and the force is 0, then cos0=1, so you can ignore that. So W=Fd as long as they're parallel and from there on you can see that potential energy is just height above the earth against the force of gravity which is just mass times acceleration due to gravity.

So that's where the U=mgh comes from.

Answer 3

As you know the work is \[W =mgh\] but be carful, h is the vertical distance from earth, so if it is 4.2 m then it is easy to calculate W from equation above. But if 4.2 is the length of the stair then you need to know the inclined angle and in that cas \[h =4.2\sin \alpha\].