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Chapter 12: Problem 6

A 220-lb man jumps out a window into a fire net \(36 \mathrm{ft}\) below. The net stretches \(4.4 \mathrm{ft}\) before bringing him to rest and tossing him back into the air. What is the potential energy of the stretched net?

Short Answer

Expert verified
The potential energy of the stretched net is approximately 1313.78 Joules.

Step by step solution

01

Convert pounds to kilograms

Firstly, it is necessary to convert the man's weight from pounds to kilograms, because the standard unit in physics for weight is the kilogram. 1 pound is approximately equal to 0.453592 kg. So, the weight of the man in kilograms is \(220 \times 0.453592 = 99.79 \, \mathrm{kg}\) (rounded to two decimal points).
02

Convert feet to meters

Similar to the weight, the lengths have to be converted from feet to meters. 1 foot is approximately equal to 0.3048 meter. Therefore, the distance the man falls is \(36 \times 0.3048 = 10.97 \, \mathrm{m}\) (rounded to two decimal points). Further, the distance the net stretches is \(4.4 \times 0.3048 = 1.34 \, \mathrm{m}\) (rounded to two decimal points).
03

Calculate the potential energy

Potential energy, usually symbolized by \(U\), is calculated using the formula \(U = m \times g \times h\), where \(m\) represents the mass (in kg), \(g\) is the gravitational acceleration (which is approximately \(9.81 \, \mathrm{m/s^2}\) on the surface of the Earth), and \(h\) indicates height (in m). In this scenario, the height is the distance the net stretches when the man falls into it. Plugging in the values gives \(U = 99.79 \times 9.81 \times 1.34 = 1313.78 \, \mathrm{J}\) (rounded to two decimal points). Thus, the potential energy of the stretched net is approximately 1313.78 Joules.

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Most popular questions from this chapter

An object falls from rest from a height \(h\). Determine the kinetic energy and the potential energy of the object as a function \((a)\) of time and \((b)\) of height. Graph the expressions and show that their sum - the total mechanical energy - is constant in each case.

A pendulum is made by tying a \(1.33-\mathrm{kg}\) stone to a string \(3.82 \mathrm{~m}\) long. The stone is projected perpendicular to the string, away from the ground, with the string at an angle of \(58.0^{\circ}\) with the vertical. It is observed to have a speed of \(8.12 \mathrm{~m} / \mathrm{s}\) when it passes its lowest point. (a) What was the speed of the stone when projected? (b) What is the largest angle with the vertical that the string will reach during the stone's motion? (c) Using the lowest point of the swing as the zero of gravitational potential energy, calculate the total mechanical energy of the system.

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To disable ballistic missiles during the early boost phase of their flight, an "electromagnetic rail gun," to be carried in low-orbit Earth satellites, has been proposed. The gun might fire a \(2.38-\mathrm{kg}\) maneuverable projectile at \(10.0 \mathrm{~km} / \mathrm{s}\). The kinetic energy carried by the projectile is sufficient on impact to disable a missile even if it carries no explosive. (A weapon of this kind is a "kinetic energy" weapon.) The projectile is accelerated to muzzle speed by electromagnetic forces. Suppose instead that we wish to fire the projectile using a spring (a "spring" weapon). What must the force constant be in order to achieve the desired speed after compressing the spring \(1.47 \mathrm{~m} ?\)

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