A hammerhead of mass \(m=2.00 \mathrm{~kg}\) is allowed to fall onto a nail from a height \(h=0.400 \mathrm{~m} .\) Calculate the maximum amount of work it could do on the nail.

Short Answer

Expert verified
Answer: The maximum amount of work the hammerhead could do on the nail is 7.848 Joules.

Step by step solution

01

Identify the given information

In this problem, the mass of the hammerhead (m) is 2.00 kg and the height (h) it falls from is 0.400 m.
02

Calculate the gravitational potential energy

To calculate the gravitational potential energy (PE), we can use the following equation: PE = m * g * h where m is the mass of the hammerhead, g is the acceleration due to gravity (approximately 9.81 \(\mathrm{m/s^2}\)), and h is the height.
03

Plug in the given values

Now, we can plug in the given values into the equation: PE = 2.00 kg * 9.81 \(\mathrm{m/s^2}\) * 0.400 m
04

Calculate the gravitational potential energy

With the values in place, we can perform the calculation: PE = 7.848 kg\(\mathrm{m^2/s^2}\)
05

Express the gravitational potential energy as work

Since gravitational potential energy and work have the same units, we can directly express the potential energy as the maximum work that can be done by the hammerhead on the nail: Maximum work = 7.848 J Therefore, the maximum amount of work the hammerhead could do on the nail is 7.848 Joules.

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