Question

power 4
you and a friend each carry a 15 kg suitcase up two flights
of stairs, walking at constant speed. take each suitcase to
be the system. suppose you carry your suitcase up the
stairs in 30 s, while your friend takes 60 s. which of the
following is true?
a) you did more work, but both of you expended the same power
b) you did more work and expended more power
c) both of you did equal work, but you required more power
d) both of you did equal work, but you required less power

Explanation:

Step1: Calculate work done

Work \(W = mgh\). Both have same \(m = 15\space kg\), \(g\) (acceleration due to gravity) and \(h\) (height of stairs). So \(W_1=W_2\) (work done is equal).

Step2: Calculate power

Power \(P=\frac{W}{t}\). Let \(W\) be the work done. For you \(t_1 = 30\space s\), for friend \(t_2=60\space s\). \(P_1=\frac{W}{30}\), \(P_2=\frac{W}{60}\). Since \(\frac{W}{30}>\frac{W}{60}\), you have more power.

Answer:

B. You did more work and expended more power