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?
To find the mechanical advantage of the simple machine, you need to use the formula 𝑀𝐴 = 𝑟𝑜𝑢𝑡𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 / 𝑖𝑛𝑛𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠.
a) To calculate the mechanical advantage:
First, we need to determine the outer radius and the inner radius of the wheel and axle.
Outer radius (𝑟𝑜𝑢𝑡𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠) = 50 cm
Inner radius (𝑖𝑛𝑛𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠) = 20 cm
Now, we can substitute these values into the formula:
𝑀𝐴 = 50 cm / 20 cm
Calculating the result:
𝑀𝐴 = 2.5
Therefore, the mechanical advantage of the simple machine is 2.5.
b) To determine the force that the worker must exert to lift the object:
We can use the formula:
Force exerted by the worker = Mechanical Advantage × Weight of the object
Substituting the values:
Force exerted by the worker = 2.5 × 2400 N
Calculating the result:
Force exerted by the worker = 6000 N
Therefore, the worker must exert a force of 6000 Newtons to lift the object.