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a 40 kilogramstudent runs up a staircase to a floor that is 5.0 meters higher than her starting point in 7.0 seconds. the student's power output is

Verified Answer :

AL2006


When she reaches the top, she has more potential energy than she had at the bottom.

         Potential energy = (mass) x (gravity) x (height)

                                     = (40 kg) x (9.8 m/s²) x (5 m)

                                     =    1,960 more joules .

         Power = (energy) / (time)

                     = (1,960 joules) / (7 seconds)

                     =         280 watts

                    (about 0.375 horsepower) 

Power is measured in Joule/s or Watt. The power output of the girl is 280 W.

Power

It can be defined as the ratio of energy to time. The formula of power is,

\(P = \dfrac Et\).................1

Where,

\(E\) - Energy

\(t\)= time = 7 s.

First, calculate the potential energy of the student,

\(PE = mgh\).............2

Where,

\(m\) - mass = 40 kg

\(g\) -  gravitational acceleration = 9.8 m/s²

\(h\) - height = 5 m

Put the values in equation 2,

\(PE = 40 \times 9.8 \times 5 \\PE = 1,960 \rm \ J\)

From equation 1,

\(P= \dfrac {1,960 }7\\\\P = 280 \rm \ W\)

Therefore, the power output of the girl is 280 W.

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