A series of four different cylinders were each subjected to a force by placing four different masses on top of them. The mass placed on each cylinder
and dimensions of each cylinder are shown below. Rank the stress on these cylinders from least to greatest.
Mass (kg) Diameter (cm) Height (cm)
Case
A
B
С
D
5.2
3.6
4.7
2.9
2.6
2.3
2.7
32.2
32.5
27.3
16.9

Answers

Answer 1

Answer:

C, B, D, A

Explanation:

Stress is F/A, where F = 9.8*mass and A = pi(d/2)^2

Do the math for each and the stress from least to greatest is C, B, D, A.

The height column is unnecessary information.

Answer 2

When four different cylinders(A,B,C,D) were each subjected to a force by placing four different masses on top of them. the Rank of stress on these cylinders from least to greatest is D, C, B, A.

What is Stress ?

Stress is defined as applied force(F) per unit cross sectional area(A) on which force is applied. it I.e. Stress = F/A. its SI unit is N/m². More force on small area leads to higher stress.

Given,

For A

Mass m = 5.2 kg

Diameter = 2.6 cm

Radius r = 1.3 cm = 0.013 m

Height =  32.5

Stress on A = Force ÷ A = mg ÷ πr²

Stress = (5.2×9.8) ÷ (3.14×0.013²)

Stress = 96031 N/m²

For B

Mass m = 3.6 kg

Diameter = 2.3 cm

Radius r = 1.15 cm = 0.011 m

Height = 27.3

Stress on B = Force ÷ A = mg ÷ πr²

Stress = (3.6 ×9.8) ÷ (3.14×0.011 ²)

Stress = 92856 N/m²

C

Mass m = 4.7 kg

Diameter = 2.7 cm

Radius r = 1.35 cm = 0.0135 m

Height = 16.9

Stress on C= Force ÷ A = mg ÷ πr²

Stress = (4.7 ×9.8) ÷ (3.14×0.0135²)

Stress = 80487 N/m²

D

Mass m = 2.9 kg

Diameter = 32.2 cm

Radius r = 16.1 cm = 0.16 m

Stress on D = Force ÷ A = mg ÷ πr²

Stress = (2.9×9.8) ÷ (3.14×0.16²)

Stress = 353 N/m²

Hence Rank of stresses on the 4 cylinders are D, C, B, A

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