From the four objects shown on the shelves, select the object that has the largest potential energy relative to the floor.
Understand the Problem
The question is asking to determine which of the four objects has the largest gravitational potential energy relative to the floor. This involves understanding the relationship between mass and height, and applying the formula for potential energy, which is PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above the floor.
Answer
The object with the largest gravitational potential energy is the School Supply Box, with a potential energy of \( 18.618 \, \text{J} \).
Answer for screen readers
The object with the largest gravitational potential energy relative to the floor is the School Supply Box, with a potential energy of ( 18.618 , \text{J} ).
Steps to Solve
- Identify the Objects and Their Heights Each object is situated at a different height from the floor. Let's define the height of each object (in meters):
- Bowl: ( h_1 = 1.0 ) m
- School supply box: ( h_2 = 2.0 ) m
- Rubber ball: ( h_3 = 1.5 ) m
- Lunchbox: ( h_4 = 0.5 ) m
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Write the Gravitational Potential Energy Formula The formula for gravitational potential energy (PE) is given by: $$ PE = mgh $$ where ( m ) is the mass (in kg), ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )), and ( h ) is the height above the floor (in meters).
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Calculate the Potential Energy for Each Object Using the formula, calculate the potential energy for each object:
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Bowl: $$ PE_1 = 0.40 \times 9.81 \times 1.0 = 3.924 , \text{J} $$
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School Supply Box: $$ PE_2 = 0.95 \times 9.81 \times 2.0 = 18.618 , \text{J} $$
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Rubber Ball: $$ PE_3 = 0.56 \times 9.81 \times 1.5 = 8.2356 , \text{J} $$
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Lunchbox: $$ PE_4 = 1.10 \times 9.81 \times 0.5 = 5.3955 , \text{J} $$
- Compare the Potential Energies Now compare the calculated potential energies:
- Bowl: ( 3.924 , \text{J} )
- School Supply Box: ( 18.618 , \text{J} )
- Rubber Ball: ( 8.2356 , \text{J} )
- Lunchbox: ( 5.3955 , \text{J} )
The object with the largest gravitational potential energy is the School Supply Box.
The object with the largest gravitational potential energy relative to the floor is the School Supply Box, with a potential energy of ( 18.618 , \text{J} ).
More Information
Gravitational potential energy depends directly on an object's mass and its height above the ground. The higher and heavier an object is, the more potential energy it has. This principle applies to various real-world scenarios, from understanding how objects fall to calculating energy for systems involving heights.
Tips
- Forgetting to include the height in the calculations can lead to incorrect results for potential energy. Always ensure height values are accurate.
- Confusing potential energy with kinetic energy or other forms of energy.
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