QuestionJuly 3, 2025

(a) How many seconds does it take a 35.0 hp motor to lift a 2800.0 Ib elevator a distance of 60.0 ft? square S (b) What was the average velocity of the elevator? square ft/s

(a) How many seconds does it take a 35.0 hp motor to lift a 2800.0 Ib elevator a distance of 60.0 ft? square S (b) What was the average velocity of the elevator? square ft/s
(a) How many seconds does it take a 35.0 hp motor to lift a 2800.0 Ib elevator a distance of 60.0 ft?
square  S
(b) What was the average velocity of the elevator?
square ft/s

Solution
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Answer

(a) 28.63 s ### (b) 2.10 ft/s Explanation 1. Convert horsepower to watts 1 hp = 746 W. Therefore, 35.0 hp = 35.0 \times 746 = 26110 W. 2. Convert pounds to kilograms 1 lb = 0.453592 kg. Therefore, 2800.0 lb = 2800.0 \times 0.453592 = 1270.058 kg. 3. Calculate the force in newtons Force (weight) = mass \times gravity = 1270.058 \times 9.81 = 12461.27 N. 4. Calculate work done Work = Force \times distance = 12461.27 \times 60.0 = 747676.2 J. 5. Calculate time using power formula **Power = \frac{Work}{Time}**. Rearrange to find Time: Time = \frac{Work}{Power} = \frac{747676.2}{26110} = 28.63 s. 6. Calculate average velocity Average velocity = \frac{\text{distance}}{\text{time}} = \frac{60.0}{28.63} = 2.10 ft/s.

Explanation

1. Convert horsepower to watts<br /> 1 hp = 746 W. Therefore, 35.0 hp = $35.0 \times 746 = 26110$ W.<br /><br />2. Convert pounds to kilograms<br /> 1 lb = 0.453592 kg. Therefore, 2800.0 lb = $2800.0 \times 0.453592 = 1270.058$ kg.<br /><br />3. Calculate the force in newtons<br /> Force (weight) = mass $\times$ gravity = $1270.058 \times 9.81 = 12461.27$ N.<br /><br />4. Calculate work done<br /> Work = Force $\times$ distance = $12461.27 \times 60.0 = 747676.2$ J.<br /><br />5. Calculate time using power formula<br /> **Power = \frac{Work}{Time}**. Rearrange to find Time: Time = $\frac{Work}{Power} = \frac{747676.2}{26110} = 28.63$ s.<br /><br />6. Calculate average velocity<br /> Average velocity = $\frac{\text{distance}}{\text{time}} = \frac{60.0}{28.63} = 2.10$ ft/s.
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