What is the power output needed from a motor to lift,in the absence of friction,a mass of 1.5 $\times$ 10⁴ kg 25 m in 6.0 s at constant speed? A)2.0 $\times$ 10⁶ W B)6.1 $\times$ 10⁵ W C)2.2 $\times$ 10⁴ W D)8.3 $\times$ 10⁵ W E)3.1 $\times$ 10⁵ W

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Quizplus · Accepted Answer

To find the power needed, we use the formula $P = \frac{W}{t}$, where $W$ is work done and $t$ is time. Work done, $W$, is given by $W = Fd$, where $F$ is the force applied and $d$ is the distance moved. Since the object is lifted at constant speed and in the absence of friction, the force applied equals the weight of the object, $F = mg$, where $m = 1.5 \times 10^4 \, \text{kg}$ and $g = 9.8 \, \text{m/s}^2$. Thus, $W = mgd = 1.5 \times 10^4 \times 9.8 \times 25$. Substituting the values and dividing by the time, $t = 6.0 \, \text{s}$, gives the power output needed. Calculating this gives a value close to $6.1 \times 10^5 \, \text{W}$.

What Is the Power Output Needed from a Motor to Lift,in