Answer:
Both of you did the same work but you expended more power.
Explanation: Ā Ā Ā Ā Ā Ā Ā
Work done by an object is calculated by force applied multiplied by the distance.
Ā W=F*d
From the figure given below let us calculate force applied bith you and yopur friend.
Let us take the stairs in positive x direction,
Work done by you Wā ,
The force applied Fā = F - mgsinĪø =maā
here aā = 0, because both of you move with constant speed
F - mgsinĪø = 0
F= Ā mgsinĪø
The work done by you on the suitcase is
W = F L cos0Ā° Ā , Ā Ā where L is he length of the staircase.
W = FL = mgsinĪøL , Ā by substituting value of F
Work done by you is Wā = mgLsinĪø
Similarly work done by your friend is Wā = mgLsinĪø.
Because both of you carry suitcase of same weight and in staircase is in same angle the force applied is same .
Therefore work done by both of you is same . Both of you did equal work.
The power , is defined as amount of energy converted or transfered per second or rate at which work is done .
P =[tex]\frac{W}{t}[/tex] =[tex]\frac{FL}{t}[/tex]
Power spend by you Pā = mgLsinĪø/t
Pā = 15*9.8*LsinĪø/30
Pā = 4.9L sinĪø Ā eqn 1
Power spend by your friend is Pā = mgLsinĪø/t
Pā =15*9.8*LsinĪø/60
Pā = 2.45LsinĪø Ā Ā eqn 2
Dividing eqn 1 and eqn 2
Pā = 2Pā
You have spend more power than your friend .
Hence Both of you did equal work but you spend more power.
