Solve Q14: Linear Dimension Question

  • Thread starter Thread starter lingkky
  • Start date Start date
  • Tags Tags
    Dimension Linear
Click For Summary
Q14 involves understanding the relationship between the linear dimensions and the resulting ratios of strength and mass for geometric shapes. The ratio of strength is determined by the ratio of cross-sectional areas divided by the mass ratio, with mass being more relevant than weight in physics. It is noted that if two triangles are similar, the area ratio is proportional to the square of the linear dimension ratio. Similarly, for cubes, the mass ratio is proportional to the cube of the linear dimension ratio. The discussion emphasizes the need for a structured approach to solving the problem, suggesting the use of a homework template for clarity.
lingkky
Messages
1
Reaction score
0
Hello everyone .I cannot understand what Q14 is asking about. May I know how to solve Q14 shown in the pic?
 

Attachments

  • IMG-20180520-WA0012.jpg
    IMG-20180520-WA0012.jpg
    39.4 KB · Views: 383
Physics news on Phys.org
The ratio of strength will be the ratio of cross-sectional areas divided by the ratio of mass (the problem says 'weight' but generally in physics it is easier to work with mass). You are told that the ants have the same shape and you can assume they are made of the same density of material. What is the ratio of the area of a triangle to a triangle that is X times bigger by linear dimension, by which we mean that each edge of the second triangle is X times the length of the corresponding edge on the first triangle?

Next imagine two cubes of granite. If the second cube has edges X times the length of those of the first cube, what is the ratio of the mass of the second to that of the first?
 
@lingkky, you'll have to repost this using the homework template, with an attempt at a solution.

Thread closed.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

Similar threads

  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 35 ·
2
Replies
35
Views
4K
Replies
2
Views
1K
Replies
3
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
1K
  • · Replies 11 ·
Replies
11
Views
807