A Student Drops A 2.20 Kg Bag Of Sugar To A Friend Who Is Standing 9.27 M Below His Apartment Window, And Whose Hands Are Held 1.56 M Above The Ground, Ready To Catch The Bag. How Much Work Is Done On The Bag By Its Weight During Its Fall Into The

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Introduction

In the realm of physics, work and energy are fundamental concepts that help us understand the behavior of objects under various forces. When a student drops a bag of sugar to a friend standing below, several forces come into play, including gravity and the weight of the bag. In this article, we will delve into the calculation of work done by the weight of the bag during its fall into the friend's hands.

Understanding Work and Energy

Before we dive into the calculation, let's briefly review the concepts of work and energy. Work is defined as the product of the force applied to an object and the distance over which the force is applied. Mathematically, work (W) is represented as:

W = F * d

where F is the force applied and d is the distance over which the force is applied.

Energy, on the other hand, is the ability to do work. There are several types of energy, including kinetic energy (the energy of motion), potential energy (stored energy), and thermal energy (energy due to temperature).

Calculating Work Done by Weight

In the case of the student dropping the bag of sugar, the weight of the bag is the primary force acting on it. As the bag falls, its weight does work on it, transferring energy from the bag to the ground. To calculate the work done by the weight of the bag, we need to consider the force of gravity acting on the bag and the distance over which this force is applied.

The force of gravity (F) acting on an object is given by:

F = m * g

where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).

The distance (d) over which the force of gravity is applied is the height from which the bag is dropped, which is 9.27 m.

Calculating the Work Done

Now that we have the force of gravity and the distance over which it is applied, we can calculate the work done by the weight of the bag:

W = F * d = (m * g) * d = (2.20 kg * 9.8 m/s^2) * 9.27 m = 204.3 J

Therefore, the work done by the weight of the bag during its fall into the friend's hands is approximately 204.3 Joules.

Considering the Catch

However, we must consider the fact that the friend's hands are held 1.56 m above the ground, ready to catch the bag. This means that the bag will not fall the entire 9.27 m distance, but rather only the distance from the point where the friend's hands are held to the ground.

To calculate the work done by the weight of the bag during this shorter distance, we need to subtract the distance from the friend's hands to the ground (1.56 m) from the total distance (9.27 m):

d = 9.27 m - 1.56 m = 7.71 m

Now, we can recalculate the work done by the weight of the bag:

W = F * d = (m * g) * d = (2.20 kg * 9.8 m/s^2) * 7.71 m = 168.3 J

Therefore, the work done by the weight of the bag during its fall into the friend's hands is approximately 168.3 Joules.

Conclusion

In conclusion, the work done by the weight of the bag during its fall into the friend's hands is approximately 168.3 Joules. This calculation takes into account the force of gravity acting on the bag and the distance over which this force is applied. By considering the catch, we can see that the work done by the weight of the bag is reduced due to the shorter distance over which the force is applied.

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

Q: What is work in the context of physics?

A: In physics, work is the product of the force applied to an object and the distance over which the force is applied. Mathematically, work (W) is represented as:

W = F * d

where F is the force applied and d is the distance over which the force is applied.

Q: What is the difference between work and energy?

A: Work is the transfer of energy from one object to another through a force applied over a distance. Energy, on the other hand, is the ability to do work. There are several types of energy, including kinetic energy (the energy of motion), potential energy (stored energy), and thermal energy (energy due to temperature).

Q: How is the force of gravity calculated?

A: The force of gravity (F) acting on an object is given by:

F = m * g

where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Q: What is the significance of the distance over which the force is applied?

A: The distance over which the force is applied is crucial in calculating the work done by the force. In the case of the student dropping the bag of sugar, the distance over which the force of gravity is applied is the height from which the bag is dropped.

Q: How is the work done by the weight of the bag calculated?

A: To calculate the work done by the weight of the bag, we need to consider the force of gravity acting on the bag and the distance over which this force is applied. The work done by the weight of the bag is given by:

W = F * d = (m * g) * d

Q: What is the effect of the friend's hands being held above the ground on the work done by the weight of the bag?

A: When the friend's hands are held above the ground, the bag will not fall the entire distance, but rather only the distance from the point where the friend's hands are held to the ground. This reduces the work done by the weight of the bag.

Q: How is the work done by the weight of the bag affected by the shorter distance over which the force is applied?

A: The work done by the weight of the bag is reduced due to the shorter distance over which the force is applied. In this case, the work done by the weight of the bag is approximately 168.3 Joules.

Q: What are some real-world applications of the concept of work and energy?

A: The concept of work and energy has numerous real-world applications, including:

  • Understanding the behavior of objects under various forces
  • Calculating the energy required to perform tasks
  • Designing efficient systems for energy transfer
  • Understanding the impact of energy on the environment

Q: What are some common misconceptions about work and energy?

A: Some common misconceptions about work and energy include:

  • Believing that work is only done when an object is moving
  • Thinking that energy is only transferred through motion
  • Assuming that work and energy are interchangeable terms

Q: How can I apply the concept of work and energy to my everyday life?

A: You can apply the concept of work and energy to your everyday life by:

  • Understanding the energy required to perform tasks
  • Designing efficient systems for energy transfer
  • Calculating the work done by various forces
  • Understanding the impact of energy on the environment

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