Question

a hydraulic system at the mechanic shop can perform up to 180,000 joules of work in a day. if throughout the day it can lift 10 cars from the ground to a height of 2 meters, how much can the cars each weigh in newtons? enter the answer

Explanation:

Step1: Recall the work formula

Work \(W = F\times d\), where \(F\) is the force (weight of the car here) and \(d\) is the distance.

Step2: Find the total work done for all cars

Given total work \(W_{total}=180000\space J\), number of cars \(n = 10\), height \(h=2\space m\).
Let the weight of each car be \(F\). The total work \(W_{total}=n\times F\times h\).

Step3: Solve for \(F\)

Rearrange the formula \(F=\frac{W_{total}}{n\times h}\).
Substitute \(W_{total} = 180000\space J\), \(n = 10\), \(h = 2\space m\) into the formula:
\(F=\frac{180000}{10\times2}\)
\(F=\frac{180000}{20}=9000\space N\)

Answer:

\(9000\)