If It Took 2 Minutes To Hoist An Aircraft Weighing 1500 Lbs To A Vertical Height Of 7 Feet, What Is The Horsepower Required For This?A. 0.45 B. 0.026 C. 0.16

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Introduction

Horsepower is a unit of measurement that represents the rate at which work is done or energy is transferred. It is commonly used to measure the power of engines, motors, and other machines. In this article, we will explore how to calculate the horsepower required to lift an aircraft weighing 1500 lbs to a vertical height of 7 feet in 2 minutes.

Understanding the Problem

The problem states that it takes 2 minutes to lift an aircraft weighing 1500 lbs to a vertical height of 7 feet. To calculate the horsepower required, we need to first calculate the work done in lifting the aircraft. Work is defined as the product of force and distance. In this case, the force required to lift the aircraft is equal to its weight, which is 1500 lbs. The distance over which the force is applied is 7 feet.

Calculating Work

To calculate the work done in lifting the aircraft, we can use the formula:

Work (W) = Force (F) x Distance (d)

In this case, the force is 1500 lbs and the distance is 7 feet. Therefore, the work done is:

W = F x d = 1500 lbs x 7 ft = 10,500 ft-lbs

Calculating Energy

The work done in lifting the aircraft is equal to the energy required to lift it. Energy is measured in units of joules (J) or foot-pounds (ft-lbs). In this case, we have calculated the work done in foot-pounds, so we can use this value as the energy required.

Calculating Power

Power is defined as the rate at which energy is transferred or work is done. It is measured in units of watts (W) or horsepower (hp). To calculate the power required to lift the aircraft, we need to divide the energy required by the time taken to lift it.

The time taken to lift the aircraft is 2 minutes, which is equal to 120 seconds. Therefore, the power required is:

P = Energy / Time = 10,500 ft-lbs / 120 s = 87.5 ft-lbs/s

Converting to Horsepower

Horsepower is a unit of measurement that is commonly used to measure the power of engines and motors. To convert the power from foot-pounds per second to horsepower, we can use the following conversion factor:

1 hp = 550 ft-lbs/s

Therefore, the power required to lift the aircraft is:

P = 87.5 ft-lbs/s / 550 ft-lbs/s/hp = 0.159 hp

Conclusion

In this article, we have calculated the horsepower required to lift an aircraft weighing 1500 lbs to a vertical height of 7 feet in 2 minutes. We have used the formula for work and energy to calculate the energy required to lift the aircraft, and then used the formula for power to calculate the power required. Finally, we have converted the power from foot-pounds per second to horsepower using the conversion factor.

Answer

The answer to the problem is 0.16 horsepower.

Discussion

This problem requires a good understanding of the concepts of work, energy, and power. It also requires the ability to apply these concepts to a real-world problem. The problem is a good example of how physics can be used to solve practical problems.

Related Topics

  • Work and energy
  • Power and efficiency
  • Physics problems and solutions

References

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Additional Resources

  • [1] Khan Academy: Work and energy
  • [2] Physics Classroom: Work and energy
  • [3] MIT OpenCourseWare: Physics 8.01: Work and energy
    Q&A: Calculating Horsepower =============================

Q: What is horsepower?

A: Horsepower is a unit of measurement that represents the rate at which work is done or energy is transferred. It is commonly used to measure the power of engines, motors, and other machines.

Q: How is horsepower calculated?

A: Horsepower is calculated by dividing the energy required to perform a task by the time taken to perform the task. The formula for horsepower is:

Horsepower (hp) = Energy (E) / Time (t)

Q: What is the difference between horsepower and watts?

A: Horsepower and watts are both units of measurement for power, but they are used in different contexts. Horsepower is commonly used to measure the power of engines and motors, while watts are used to measure the power of electrical devices.

Q: How is horsepower related to foot-pounds per second?

A: Horsepower is related to foot-pounds per second (ft-lbs/s) by the following conversion factor:

1 hp = 550 ft-lbs/s

Q: Can you give an example of how to calculate horsepower?

A: Let's say we want to calculate the horsepower required to lift a 1500 lb weight to a height of 7 feet in 2 minutes. First, we need to calculate the work done in lifting the weight:

Work (W) = Force (F) x Distance (d) = 1500 lb x 7 ft = 10,500 ft-lbs

Next, we need to calculate the time taken to lift the weight:

Time (t) = 2 minutes x 60 seconds/minute = 120 seconds

Finally, we can calculate the horsepower required:

Horsepower (hp) = Energy (E) / Time (t) = 10,500 ft-lbs / 120 s = 87.5 ft-lbs/s = 0.159 hp

Q: What are some common applications of horsepower?

A: Horsepower is commonly used to measure the power of engines, motors, and other machines. Some common applications of horsepower include:

  • Measuring the power of engines in vehicles
  • Measuring the power of motors in industrial equipment
  • Measuring the power of generators and pumps
  • Measuring the power of air conditioning and refrigeration systems

Q: Can you give some examples of horsepower in real-world applications?

A: Here are a few examples of horsepower in real-world applications:

  • A typical car engine produces around 100-200 horsepower
  • A small electric motor might produce around 1-5 horsepower
  • A large industrial generator might produce around 1000-5000 horsepower
  • A large air conditioning system might produce around 10-50 horsepower

Q: What are some common mistakes to avoid when calculating horsepower?

A: Here are a few common mistakes to avoid when calculating horsepower:

  • Failing to convert units correctly (e.g. ft-lbs/s to hp)
  • Failing to account for losses and inefficiencies in the system
  • Failing to use the correct formula for horsepower
  • Failing to check units and dimensions carefully

Q: Where can I learn more about horsepower and its applications?

A: There are many resources available to learn more about horsepower and its applications, including:

  • Online tutorials and courses
  • Textbooks and reference books
  • Industry publications and trade magazines
  • Online forums and discussion groups

Conclusion

Horsepower is an important unit of measurement in many fields, including engineering, physics, and industry. By understanding how to calculate horsepower and its applications, you can better understand the power of engines, motors, and other machines.