A car jack with a mechanical advantage of 6 needs to produce an output force of 600 N to raise a car. What input force is required?
A. 6 N
B. 100 N
C. 600 N
D. $3,600 N$
Answer (2)
The mechanical advantage (MA) is the ratio of output force to input force: M A = F in F o u t .
Rearrange the formula to solve for the input force: F in = M A F o u t .
Substitute the given values: F in = 6 600 N .
Calculate the input force: F in = 100 N . The required input force is 100 N .
Explanation
Understanding the Problem We are given a car jack with a mechanical advantage of 6. This means that the jack multiplies the input force by a factor of 6 to produce the output force. We are also given that the output force required to lift the car is 600 N. Our goal is to find the input force needed to achieve this.
Stating the Formula The mechanical advantage (MA) is defined as the ratio of the output force ( F o u t ) to the input force ( F in ). The formula is: M A = F in F o u t We are given M A = 6 and F o u t = 600 N . We need to find F in .
Calculating the Input Force We can rearrange the formula to solve for the input force: F in = M A F o u t Now, we substitute the given values into the formula: F in = 6 600 N F in = 100 N
Final Answer Therefore, the input force required is 100 N.
Examples
Car jacks are a practical application of mechanical advantage. Imagine you need to lift a heavy object, like a car, to change a tire. Without a car jack, you'd need to apply a very large force directly. However, a car jack, with its mechanical advantage, allows you to apply a much smaller force over a longer distance to achieve the same result. For example, if a car jack has a mechanical advantage of 6, it means you only need to apply 1/6th of the force that would be required without it. This makes lifting heavy objects much easier and safer.
The input force required to produce an output force of 600 N with a car jack that has a mechanical advantage of 6 is 100 N. This is calculated using the formula for mechanical advantage. Thus, the correct answer is B. 100 N.
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