Dimensional Analysis: Solving E = (1/2) mv Equation

In summary, the conversation discussed the dimensionality of the equation E = (1/2)mv, where E represents energy, m represents mass, and v represents speed. The equation was found to be incorrect as the left side contains extra length and time units that the right side does not have. Therefore, the correct version of the equation, E = (1/2)mv^2, is dimensionally correct.
  • #1
Michele Nunes
42
2

Homework Statement


Is the following equation dimensionally correct?

Homework Equations


E = (1/2) mv
where:
E = energy
m = mass
v = speed

The Attempt at a Solution


1. I understand that the 1/2 is irrelevant.
2. I broke everything down into length, time, and mass.
3. I got ML^2/T^2 = ML/T
4. My confusion is that if you square L and T on the left side, you still have length and time so I mean essentially, you have the same types of quantities on both sides of the equation in the same order, so I want to say it is correct, however the fact that L and T are squared on the left side but not on the right side bugs me and I'm doubtful.
 
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  • #2
Michele Nunes said:

Homework Statement


Is the following equation dimensionally correct?

By "the following equation" do you mean E=(1/2)mv^2 ?
 
  • #3
C. Lee said:
By "the following equation" do you mean E=(1/2)mv^2 ?
I was referring to the equation under Relevant Equations (my apologies, should've clarified that), which is E=(1/2)mv
 
  • #4
Michele Nunes said:
I was referring to the equation under Relevant Equations (my apologies, should've clarified that), which is E=(1/2)mv

You are missing ^2 at the end of the equation: it should be E = (1/2)mv^2.
 
  • #5
C. Lee said:
You are missing ^2 at the end of the equation: it should be E = (1/2)mv^2.
Okay so it isn't dimensionally correct? The book just gives me an equation (it's not necessarily supposed to be right or wrong) and I'm just supposed to say whether the given equation is dimensionally correct. But since the equation itself is wrong then I'm going to assume that the correct version is dimensionally correct and this one is not.
 
  • #6
Michele Nunes said:
Okay so it isn't dimensionally correct? The book just gives me an equation (it's not necessarily supposed to be right or wrong) and I'm just supposed to say whether the given equation is dimensionally correct. But since the equation itself is wrong then I'm going to assume that the correct version is dimensionally correct and this one is not.

Absolutely right. As you have pointed out from the beginning LHS has extra L/T that RHS does not have, therefore it cannot be dimensionally correct.
 
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What is Simple Dimensional Analysis?

Simple Dimensional Analysis is a method used in science to convert units of measurement and perform calculations. It involves manipulating the units of measurement and using conversion factors to ensure that the final answer has the correct units.

Why is Simple Dimensional Analysis important in science?

Simple Dimensional Analysis is important in science because it allows for accurate and consistent measurements and calculations. It also helps to ensure that the final answer has the correct units, making it easier to interpret and compare with other data.

What are the steps involved in Simple Dimensional Analysis?

The steps involved in Simple Dimensional Analysis are:
1. Identify the given measurement with its associated units
2. Determine the desired units for the final answer
3. Set up a conversion factor to convert between the given units and desired units
4. Cancel out the given units with the conversion factor
5. Perform any necessary arithmetic operations
6. Check that the units in the final answer are correct and make sense.

How do you choose the appropriate conversion factor in Simple Dimensional Analysis?

To choose the appropriate conversion factor, you must first identify the given units and the desired units for the final answer. Then, you can use a conversion chart or conversion equation to find the correct conversion factor. It is important to make sure that the conversion factor is set up so that the given units cancel out and the desired units are left in the final answer.

What are some tips for using Simple Dimensional Analysis effectively?

Some tips for using Simple Dimensional Analysis effectively include:
- Write out all units and ensure they are in the correct order
- Use a conversion chart or equation to find the appropriate conversion factor
- Keep track of units and make sure they cancel out correctly
- Use scientific notation to simplify calculations with large or small numbers
- Double check the final answer to make sure the units are correct and make sense.

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