How can I prove i = j = k = 1 in Peter's energy equation?

  • Thread starter Panphobia
  • Start date
In summary, Peter has introduced a new energy equation with four variables - mass, acceleration, distance, and a dimensionless constant. The question is to prove that the exponents of these variables are all equal to 1. Using dimensional analysis, we can express energy in terms of mass, length, and time, which can help us solve the problem. After receiving help and hints, the person was able to figure out the solution.
  • #1
Panphobia
435
13
I have been stuck on this problem for a while, I was looking at questions in a textbook, and could not figure this question out

"Peter came out with a new energy equation
E = (C)(M^i)(a^j)(d^k)
M is mass, a is acceleration, d is distance, and C is a dimensionless constant,
prove that i = j = k = 1"

How would you even start with this?

Regards, Panphobia
 
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  • #2
Hint: dimensional analysis
 
  • #3
I know that dimensional analysis is being able to state Mass, Length, and Time in terms of each other. But I do not know how that helps me prove that i = j = k = 1.
 
  • #4
Write the dimension of energy, by means of the dimensions of mass, length and time!
 
  • #5
Thank you everyone that helped me and gave me hints, I figured it out!
 

1. What does it mean to prove that i = j = k = 1?

Proving that i = j = k = 1 means showing that all three variables (i, j, and k) have the value of 1. This could involve using mathematical equations or logical reasoning to demonstrate that the variables are equal to 1.

2. Why is it important to prove that i = j = k = 1?

Proving that i = j = k = 1 can be important in certain scientific experiments or calculations where the values of these variables have a significant impact on the results. It can also help to validate the accuracy of a hypothesis or theory.

3. What methods can be used to prove that i = j = k = 1?

There are various methods that can be used to prove that i = j = k = 1, depending on the context and the specific variables involved. These may include algebraic manipulation, substitution, or logical deduction.

4. Can i = j = k = 1 be proven in different ways?

Yes, there can be multiple ways to prove that i = j = k = 1. The specific method used will depend on the variables and the purpose of the proof. However, all valid proofs should ultimately lead to the conclusion that i = j = k = 1.

5. What are the implications of i = j = k = 1 being proven?

The implications of proving that i = j = k = 1 will depend on the specific context and the reasons for proving it. In some cases, it may validate a scientific theory or support the accuracy of a mathematical model. In other cases, it may have practical implications for solving problems or making predictions.

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