Question

two identical motors, motor x and motor y, lift the same 100 kg mass to the same 10 m height. motor x takes 5 seconds, and motor y takes 10 seconds. which statement is true? motor x performs more work than motor y. motor x has a higher power output than motor y. motor x and motor y have the same power output. motor y performs more work than motor x.

Explanation:

Step1: Calculate work done by each motor

Work \(W = mgh\). Here, \(m = 100\space kg\), \(g= 9.8\space m/s^{2}\), \(h = 10\space m\).
For Motor X: \(W_{X}=100\times9.8\times10 = 9800\space J\)
For Motor Y: \(W_{Y}=100\times9.8\times10 = 9800\space J\)
So, \(W_{X}=W_{Y}\)

Step2: Calculate power of each motor

Power \(P=\frac{W}{t}\)
For Motor X: \(P_{X}=\frac{9800}{5}=1960\space W\)
For Motor Y: \(P_{Y}=\frac{9800}{10} = 980\space W\)
Since \(1960>980\), \(P_{X}>P_{Y}\)

Answer:

Motor X has a higher power output than Motor Y.