The depth x to which a bullet penetrates a human body depends upon coefficient of Elasticity. and kinetic energy by the method of dimensions. show that.
Well, well, well, someone wants to get all technical, huh? Alright, let's give it a shot!
Let's start by looking at the coefficient of elasticity, which measures how rigid or stretchy a material is. Now, imagine a bullet trying to penetrate a human body. If the body is as stiff as a board, the bullet may not penetrate as deep. But if the body is as stretchy as a rubber band, the bullet might just go through like a hot knife through butter.
Next up, we've got kinetic energy, which is all about motion and velocity. A bullet carrying loads of kinetic energy will have a lot of force behind it, which can result in deeper penetration. It's like the bullet saying, "Move aside, puny human, I've got places to go!"
Now, let's bring in the method of dimensions, which is like a fancy math superhero. This method helps us understand how physical quantities relate to each other. In this case, we can say that the depth of bullet penetration (let's call it "D") depends on both the coefficient of elasticity (let's call it "E") and the kinetic energy (let's call it "K").
So, using the method of dimensions, we can express this relationship as:
D ∝ E^K
Here, the "^" symbol means "to the power of." That equation shows us that the depth of penetration is directly proportional to the coefficient of elasticity raised to the power of kinetic energy.
So there you have it! The depth to which a bullet penetrates a human body depends on the coefficient of elasticity and kinetic energy, all thanks to the method of dimensions. Just remember, when it comes to bullets and human bodies, it's always best to crack a joke instead of letting things get too serious!
To show the relationship between the depth of penetration of a bullet into a human body and the coefficient of Elasticity, as well as kinetic energy, we can use the method of dimensional analysis.
Step 1: Identify the variables and their dimensions:
Let's denote the depth of penetration as "d", the coefficient of elasticity as "E", and the kinetic energy as "K". We need to determine the dimensions of each of these variables.
The dimensions of depth (d) are typically represented as [L], which stands for length.
The dimensions of coefficient of elasticity (E) are represented as [M][L]^-1[T]^-2, where [M] stands for mass, [L] stands for length and [T] stands for time.
The dimensions of kinetic energy (K) are represented as [M][L]^2[T]^-2.
Step 2: Apply the principle of homogeneity:
According to the principle of homogeneity, all terms in an equation must have the same dimensions. Therefore, the dimensions on the left-hand side (LHS) of the equation must be equal to the dimensions on the right-hand side (RHS).
Step 3: Set up the equation:
We can correlate the depth (d), coefficient of elasticity (E), and kinetic energy (K) using the equation:
d = E^a * K^b
Step 4: Solve for the exponents:
To determine the exponents "a" and "b", we equate the dimensions on the LHS and RHS of the equation.
For length [L]:
LHS = [L] = E^a * K^b
RHS = [L] = [M][L]^-1[T]^-2^a * [M][L]^2[T]^-2^b
Comparing the exponents of the variables, we can equate them:
a * (-1) + 2b = 0
For mass [M]:
LHS = [M]^0
RHS = [M]^1 * [M]^1
Comparing the exponents again, we get:
a + b = 0
For time [T]:
LHS = [T]^0
RHS = [T]^-2^a * [T]^-2^b
Comparing the exponents again, we get:
-2a - 2b = 0
Step 5: Solve the system of equations:
Using the equations we obtained in Step 4, we can solve for the values of "a" and "b".
From the equation a * (-1) + 2b = 0, we can solve for "a" in terms of "b":
a = 2b
Substituting this in the equation a + b = 0:
2b + b = 0
3b = 0
b = 0
Plugging this value of "b" back into a = 2b:
a = 2(0)
a = 0
Step 6: Express the equation using the values of "a" and "b":
Since both "a" and "b" are equal to 0, the equation becomes:
d = E^0 * K^0
d = 1
Step 7: Final result:
The equation simplifies to:
d = 1
Therefore, the depth of penetration (d) of a bullet into a human body is independent of both the coefficient of elasticity (E) and the kinetic energy (K).