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Chapter 3: Problem 18

If \(1 \mathrm{~kg}\) blocks were stacked one upon the other starting at the surface of the earth and continuing forever into space, the blocks near the bottom of the stack would have: A. less gravitational potential encigy than blocks at the middlle or blocks near the top of the stack. B. less gravitational potential energy than blocks at the middle and the same gravitational energy as blocks near the top of the stack. C. the same gravitational potential energy as all other blocks. D. more gravitational potential energy than blocks at the middle or blocks near the top of the stack.

Short Answer

Expert verified
A. less gravitational potential energy than blocks at the middle or blocks near the top of the stack.

Step by step solution

01

Understand the Concept of Gravitational Potential Energy

Gravitational potential energy (GPE) is given by the formula: \[GPE = mgh\] where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is the height above the reference point. GPE increases with height.
02

Identify the Relationship Between Height and GPE

Since GPE increases with height, the higher a block is above the Earth's surface, the more gravitational potential energy it possesses. Blocks near the bottom of the stack have less height \(h\) compared to blocks in the middle or near the top.
03

Compare GPE of Blocks at Different Positions

Blocks at the bottom of the stack have less GPE because their height \(h\) is small. Blocks in the middle have a moderate height \(h\), and blocks near the top have the greatest height \(h\). Therefore, blocks at the middle and top of the stack have more GPE than blocks near the bottom.
04

Conclusion Based on Comparison

Given the previous comparison, the blocks near the bottom have less gravitational potential energy than those at the middle or top. This matches with option A.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gravitational Potential Energy Formula
Gravitational potential energy (GPE) is a measure of the energy an object possesses due to its position in a gravitational field. The GPE formula is: \[GPE = mgh\]
In this formula, \(m\) represents mass, \(g\) is the acceleration due to gravity (which is approximately \(9.8 \text{ m/s}^2\) on Earth), and \(h\) is the height of the object above a reference point. This formula shows that GPE is directly proportional to both the mass of the object and its height above the ground.By knowing the mass and height, one can easily calculate the GPE, which reflects how much energy is stored due to an object's elevated position in a gravitational field.
Height and GPE Relationship
The height of an object plays a crucial role in determining its gravitational potential energy. As the height \(h\) increases, the GPE also increases proportionally.
  • When an object is higher up, it has more energy stored due to gravity, which can be converted into kinetic energy if the object falls.
  • This explains why blocks at the top of a stack have more GPE than those at the bottom.
  • Conversely, the closer the object is to the ground, the lower its GPE.
Understanding how height affects GPE helps in various applications, such as engineering, where the stability of structures is dependent on how gravitational energy is distributed.
Energy Concepts in Physics
Energy concepts in physics are fundamental for describing the behavior of objects. One such concept is gravitational potential energy, which is a type of mechanical energy. Mechanical energy can be categorized into kinetic energy (energy of motion) and potential energy (stored energy).
  • Gravitational potential energy is a form of potential energy.
  • It depends on the position of an object in a gravitational field.
  • As an object gains height, it stores more energy.
In physics, understanding energy is vital for solving problems related to motion, forces, and the conservation of energy. The law of conservation of energy states that energy cannot be created or destroyed but can be transformed from one form to another.
Stacked Masses and Gravitational Effects
When considering stacked masses, it's important to recognize that gravitational potential energy varies with height.
  • Each block in a stack has a different height, resulting in varying GPE.
  • Blocks at the bottom of the stack have less GPE because their height is lower.
  • Blocks in the middle have moderate GPE, and blocks near the top have the highest GPE.
This variation in energy influences how gravitational forces exert pressure on the structure itself, affecting its stability. Therefore, in tall structures or stacks, engineers must consider how the distribution of mass and height impacts gravitational potential energy to ensure safety and stability.

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Most popular questions from this chapter

A meteor with a mass of \(1 \mathrm{~kg}\) moving at \(20 \mathrm{~km} / \mathrm{s}\) collides with Jupiter's atmosphere. The meteor penetrates \(100 \mathrm{~km}\) into the atmosphere and disintegrates. What is the average force on the meteor once it enters Jupiter's atmosphere? (Note: ignore gravity) A. \(2 \times 10^3 \mathrm{~N}\) B. \(4 \times 10^3 \mathrm{~N}\) C. \(8 \times 10^3 \mathrm{~N}\) D. \(2 \times 10^9 \mathrm{~N}\)

A carpenter who is having a difficult time loosening a serew puts away his screwdriver and chooses another with a bandle with a larger diameter. He does this because: A. increasing force increases torque- B. decreasing force decreases torque. C. increasing lever arm increases torque. D. decreasing lever am decreases torque.

A circus tightrope walker wishes to make his rope as straight as possible when he walks across it. If the tightrope walker has a mass of \(75 \mathrm{~kg}\), and the rope is 150 \(\mathrm{m}\) long, how much tension must be in the rope in order to make it perfectly straight? A. \(0 \mathrm{~N}\) B. \(\quad 750 \mathrm{~N}\) C. \(1500 \mathrm{~N}\) D. No amount of tension in the rope could make it perfectly straight.

Which of the following describes a situation requiring no net force? A. A car starts from rest and reaches a speed of 80 \(\mathrm{km} / \mathrm{hr}\) after 15 seconds. B. A bucket is lowered from a rooftop at a constant speed of \(2 \mathrm{~m} / \mathrm{s}\). C. A skater glides along the ice, gradually slowing from \(10 \mathrm{~m} / \mathrm{s}\) to \(5 \mathrm{~m} / \mathrm{s}\). D. The pendulum of a clock moves back and forth at a constant frequency of \(0.5\) cycles per second.

A winch is used to lift heavy objects to the top of building under construction. A winch with a power of \(50 \mathrm{~kW}\) was replaced with a new winch with a power of \(100 \mathrm{~kW}\). Which of the following statements about the new winch is NOT true? A. The new winch can do twice as much work in the same time as the old winch. B. The new winch takes twice as much time to do the same work as the old winch. C. The new winch can raise objects with twice as much mass at the same speed as the old winch. D. The new winch can raise objects with the same mass at twice the speed of the old winch.
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