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Chapter 7: Problem 14

You fly from Boston's Logan Airport, at sea level, to Denver, altitude \(1.6 \mathrm{km}\). Taking your mass as \(65 \mathrm{kg}\) and the zero of potential energy at Boston, what's your gravitational potential energy (a) at the plane's 11 -km cruising altitude and (b) in Denver?

Short Answer

Expert verified
The gravitational potential energy at 11 km altitude is 7,007,000 Joules and in Denver, it is 1,024,000 Joules.

Step by step solution

01

Convert Kilometers to Meters

First, convert the altitudes from kilometers to meters (since the values of \( g \) and \( m \) are in m/s² and kg respectively). For 11 km, 1 kilometer equals 1000 meters, hence, 11 km = 11000 meters. Similarly, 1.6 km = 1600 meters.
02

Calculate Potential Energy at 11 km

Next, calculate the potential energy at 11 km altitude using the formula \( PE = mgh \). Substitute the values into the formula to find the solution. So, \( PE = 65 kg \times 9.8 m/s² \times 11000 m = 7,007,000 J \). Hence, the gravitational potential energy at 11 km altitude is 7,007,000 Joules.
03

Calculate Potential Energy in Denver

Finally, calculate the potential energy in Denver. The altitude is 1.6 km, which equals 1600 meters. Substitute this value into the formula \( PE = mgh \). So, \( PE = 65 kg \times 9.8 m/s² \times 1600 m = 1,024,000 J \). The gravitational potential energy in Denver is therefore 1,024,000 Joules.

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Most popular questions from this chapter

A \(10.000-\mathrm{kg}\) Navy jet lands on an aircraft carrier and snags a cable to slow it down. The cable is attached to a spring with \(k=40 \mathrm{kN} / \mathrm{m} .\) If the spring stretches \(25 \mathrm{m}\) to stop the plane, what was its landing speed?

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