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Chapter 5: Problem 25

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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Most popular questions from this chapter

An engine pumps water continuously through a hose. If the speed with which the water passes through the hose nozzle is \(v\) and if \(k\) is the mass per unit length of the water jet as it leaves the nozzle, what is the kinetic energy being imparted to the water? a) \(\frac{1}{2} k v^{3}\) c) \(\frac{1}{2} k v\) e) \(\frac{1}{2} v^{3} / k\) b) \(\frac{1}{2} k v^{2}\) d) \(\frac{1}{2} v^{2} / k\)

At sea level, a nitrogen molecule in the air has an average kinetic energy of \(6.2 \cdot 10^{-21}\) J. Its mass is \(4.7 \cdot 10^{-26} \mathrm{~kg}\). If the molecule could shoot straight up without colliding with other molecules, how high would it rise? What percentage of the Earth's radius is this height? What is the molecule's initial speed? (Assume that you can use \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\); although we'll see in Chapter 12 that this assumption may not be justified for this situation.

How much work do movers do (horizontally) in pushing a \(150-\mathrm{kg}\) crate \(12.3 \mathrm{~m}\) across a floor at constant speed if the coefficient of friction is \(0.70 ?\) a) 1300 J c) \(1.3 \cdot 10^{4}\) ] e) 130 ] b) 1845 J d) \(1.8 \cdot 10^{4}\) ]

A limo is moving at a speed of \(100 . \mathrm{km} / \mathrm{h}\). If the mass of the limo, including passengers, is \(1900 . \mathrm{kg},\) what is its kinetic energy?

How much work is done against gravity in lifting a \(6.00-\mathrm{kg}\) weight through a distance of \(20.0 \mathrm{~cm} ?\)
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