Physics

Problem

An electric motor operates in two distinct modes while lifting a small mass vertically. • Mode I: The motor supplies a constant

50\,\text{W}

of power for the first

5.0\,\text{s}

. • Mode II: Immediately afterward, it supplies a constant

120\,\text{W}

of power for the next

3.0\,\text{s}

. Assume all the motor’s output power is converted into gravitational potential energy of the mass. (a) Calculate the work done by the motor during Mode I. (b) Calculate the work done by the motor during Mode II. (c) Determine the total increase in gravitational potential energy of the mass after the full

8.0\,\text{s}

of operation, and state the result with appropriate units.

Intuitive explanation

The key is recognizing that power tells you the rate of energy delivery, not the total energy itself. Since all power goes into lifting (gaining gravitational potential energy $\Delta PE = mgh$ ), you'll calculate the total energy added in each mode separately, then use that energy to find how high the mass rises overall. The work-energy connection— $P = \frac{W}{t}$ , so $W = Pt$ —is your bridge from power and time to the height climbed.

Intuitive explanation

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