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Chapter 3: Problem 70

Determine the work done by a crane lifting a 2400 -pound car 5 feet.

Short Answer

Expert verified
The work done by the crane is 386400 foot-pounds.

Step by step solution

01

Calculate the weight of the car

The weight of an object is calculated by the product of its mass and the acceleration due to gravity. In this case, the mass of the car is 2400 pounds and the gravity is 32.2 ft/s虏. Therefore the weight F of the car becomes \( F = m \cdot g = 2400 \cdot 32.2 = 77280 \) pound-foot/s虏.
02

Calculate the work done

The work done is calculated as the product of the force applied (weight of the car) and the distance over which it is applied (height the car is lifted). In this case, the force (weight) is 77280 pound-foot/s虏 and the distance is 5 feet. So the work done \( W = F \cdot d = 77280 \cdot 5 = 386400 \) pound-foot鲁/s虏
03

Convert to standard unit

The standard unit of work done is Joules in the SI system (1 Joule = 1 Newton-meter). However, since this problem is stated in English units (pounds and feet), it is permissible to leave the answer in foot-pounds. The conversion factor from pound-foot鲁/s虏 to foot-pounds is 1 pound-foot鲁/s虏 = 1 foot-pound. Thus the work done is \( W = 386400 \) foot-pounds.

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