Center of Mass question (help)?

[driftk]

I tried this problem but only managed to somewhat understand Part A. But that answer is wrong as well, so can someone guide me through steps of finding the answer: Thank you.

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 0.92 m long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0 Kg person, the mass of the upper leg would be 8.60 Kg, while that of the lower leg (including the foot) would be 5.25 Kg.

A. Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally.

- i got 0.35 as my answer but it was wrong. My method was this: (5.25*0.92)/ total mass of 13.85. What am I doing wrong?

B. Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is bent at the knee to form a right angle with the upper leg remaining horizontal.

 

[LowlyPion]

I tried this problem but only managed to somewhat understand Part A. But that answer is wrong as well, so can someone guide me through steps of finding the answer: Thank you.

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 0.92 m long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0 Kg person, the mass of the upper leg would be 8.60 Kg, while that of the lower leg (including the foot) would be 5.25 Kg.

A. Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally.

- i got 0.35 as my answer but it was wrong. My method was this: (5.25*0.92)/ total mass of 13.85. What am I doing wrong?

B. Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is bent at the knee to form a right angle with the upper leg remaining horizontal.

The Center of Mass is the ∑ m*x/ ∑ m

What they want you to do is calculate the CoM using both the two leg parts, upper and lower. Since they say that each piece is uniform, then you can assume that the CoM's of each piece are located half way on each part.

 

[nlightner]

I am happy to assist you with this problem. Let's break down the steps to finding the center of mass for this leg.

First, we need to understand what the center of mass is. It is the point at which the body's mass is evenly distributed in all directions. In simpler terms, it is the point where an object would balance perfectly if placed on a pivot.

Now, let's look at Part A. You correctly calculated the mass of the lower leg (including the foot) as 5.25 Kg. However, your calculation for the x-coordinate of the center of mass is not correct. The formula for finding the center of mass is:

x_cm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)

In this case, we have two masses (upper leg and lower leg) and two corresponding x-coordinates (0 and 0.92). Plugging in the values, we get:

x_cm = (8.60*0 + 5.25*0.92) / (8.60 + 5.25)

= 4.83 / 13.85

= 0.35 m

So, your answer of 0.35 m is correct for Part A. It is possible that you made a mistake in your calculation or inputting the values, leading to an incorrect answer. I would suggest double-checking your work to find the error.

Moving on to Part B, we need to consider the bent knee. In this case, the upper leg and lower leg will have different x-coordinates. Let's call the x-coordinate of the center of mass for the upper leg as x1 and for the lower leg as x2. We can set up the following equation:

m1x1 + m2x2 = (m1 + m2) * x_cm

Plugging in the values, we get:

8.60*x1 + 5.25*x2 = 13.85 * x_cm

We also know that the total length of the leg is 0.92 m, so we can set up another equation:

x1 + x2 = 0.92

Solving these two equations simultaneously, we get:

x1 = 0.92 - x2

Substituting this value in the first equation, we get:

8.60