A worker uses awhell and axle with inner radius of 20cm and outer of 50 cm to lift a 2400N object.
a) What is the mechanical advantage of the simple machine?
b) What force must the worker exert to lift the object?
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50/20
To find the mechanical advantage of the simple machine, we can use the formula:
Mechanical Advantage = Output force / Input force
In this case, the output force is the weight of the object, which is given as 2400N. To find the input force, we need to determine the effective radius of the wheel and axle system.
The effective radius is the average of the inner and outer radii:
Effective radius = (Inner radius + Outer radius) / 2
Plugging in the values:
Effective radius = (20 cm + 50 cm) / 2 = 35 cm
However, it's important to note that all values should be in the same units. Therefore, we need to convert centimeters to meters:
Effective radius = 35 cm = 0.35 m
Now that we have the effective radius, we can calculate the mechanical advantage:
Mechanical Advantage = Output force / Input force
Mechanical Advantage = 2400N / Input force
To solve for the input force, we rearrange the equation:
Input force = Output force / Mechanical Advantage
Input force = 2400N / Mechanical Advantage
For part (a), we've determined the input force, which depends on the mechanical advantage of the simple machine.
To find the force that the worker must exert to lift the object, we need to calculate the input force. We'll use the formula:
Input force = Output force / Mechanical Advantage
Plugging in the given values:
Input force = 2400N / Mechanical Advantage
Therefore, to answer part (b), we need to calculate the mechanical advantage first.