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Chapter 11: Problem 28

Calculate the kinetic energies of the following objects moving at the given speeds: ( \(a\) ) a \(110-\mathrm{kg}\) football linebacker running at \(8.1 \mathrm{~m} / \mathrm{s} ;\) (b) a \(4.2-\mathrm{g}\) bullet at \(950 \mathrm{~m} / \mathrm{s} ;\) ( \(c\) ) the aircraft carrier Nimitz, 91,400 tons at \(32.0\) knots.

Short Answer

Expert verified
The kinetic energy of the linebacker is approximately \(3614.5 \, J\), the bullet approximately \(1898.25 \, J\), and the aircraft carrier approximately \(2.287 \times 10^{11} \, J\).

Step by step solution

01

Calculate the Kinetic Energy of the Linebacker

First, convert the mass of the linebacker to kg, if not already in this unit. In this case, it is. Then, plug the values into the kinetic energy formula to solve for the linebacker's kinetic energy: \(KE = \frac{1}{2}mu^2 = \frac{1}{2}(110 \, kg)(8.1 \, m/s)^2\)
02

Calculate the Kinetic Energy of the Bullet

The mass of the bullet is given in grams, so it needs to be converted to kilograms by dividing by 1,000. After that, calculate the kinetic energy of the bullet by plugging the values into the kinetic energy formula: \(KE = \frac{1}{2}mu^2 = \frac{1}{2}(0.0042 \, kg)(950 \, m/s)^2.\)
03

Calculate the Kinetic Energy of the Aircraft Carrier

First, convert the mass of the aircraft carrier from tons to kilograms by multiplying by 1,000. The speed is given in knots, it needs to be converted to meters per second by multiplying by 0.51444 (since 1 knot = 0.51444 m/s). Now with values in the appropriate units, you can solve for the kinetic energy with the formula: \(KE = \frac{1}{2}mu^2 = \frac{1}{2}(91400000 \, kg)(32 \times 0.51444 \, m/s)^2\)

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Most popular questions from this chapter

A worker pushed a \(58.7\) -lb block \((m=26.6 \mathrm{~kg})\) a distance of \(31.3 \mathrm{ft}(=9.54 \mathrm{~m})\) along a level floor at constant speed with a force directed \(32.0^{\circ}\) below the horizontal. The coefficient of kinetic friction is \(0.21\). How much work did the worker do on the block?

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