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A 17 kg box sitting on a shelf has a potential energy of 350 j. how high is the shelf? round your answer to the nearest whole number.
The Correct answer is 2 meters
Explanation
1. Formula for potential energy:
The potential energy (PE) of an object due to gravity is given by the formula:
PE = mgh
where:
- m is the mass of the object (17 kg in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s²)
- h is the height of the object above a reference point (the shelf in this case)
2. Solve for h:
We are given PE = 350 J and m = 17 kg. We want to find h.
Rearrange the formula to solve for h:
h = PE / (mg)
Substitute the known values:
h = 350 J / (17 kg * 9.8 m/s²)
h ≈ 2.21 m
3. Round to the nearest whole number:
h ≈ 2 meters
Therefore, the shelf is approximately 2 meters high.
Potential Energy
In mathematics, potential energy is a concept often used in physics and related fields to describe the energy that an object has due to its position or configuration. It is defined as the energy an object has because of its position relative to other objects. The formula for potential energy depends on the context but generally involves the mass of the object, the acceleration due to gravity, and the height or distance the object is from a reference point.
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In mechanics, the potential energy U of an object near the surface of the Earth is often given by the formula:
U=mgh
Where:
- U is the potential energy,
- m is the mass of the object,
- g is the acceleration due to gravity (approximately 9.81 m)
- ℎh is the height of the object above a reference point.
This formula tells us that the potential energy of an object increases with its mass, the acceleration due to gravity, and its height above the reference point.
Potential energy is an important concept in physics and is used to analyze and understand the behavior of objects in various physical systems, such as pendulums, springs, and gravitational fields.
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