Question

3. A cube of Brass (B = 70 GPa) measuring 1.0 m on each side is submerged under water. It is lowerd to a depth where a force "F" is acting perpendicularly into each side, reduces the cube's volume by 1.8 %.

(a) Calculate the size of this force.

2.A researcher examines a piece of fresh human cartilage, with an area of 1.9 cm2. She observes that when subjected to a tensile force of 194 N it stretches by 4.8 %.

(a) Calculate the elastic modulus of cartilage.

1. A student pushes on the end of a helical spring, which in turn presses a 1.25 kg, wooden block onto a vertical wall. The coefficient of static friction between the block and wall is 0.5. She compresses the spring 5.2 cm.

(a) Calculate the minimum spring constant necessaary to prevent the block from sliding down the wall.

Answer 1

Problem # 3

DATA:

Solution

The volumetric volume is defined as:

Isolating from equation (1) we have:

Where:

is the volumetric volume

is the Area of the one side of cube, which is defined as:

is the change in volume, so:

is the initial volume, which can be obtained using:

Now, replacing data given values into equation (5) we have:

Solving we obtain:

Now, the final volume is reduced by 1.8 % so:

Inserting (7) into equation (8) we have:

Inserting (9) and (7) into equation (4) we have:

Solving we obtain:

Now, the area can be obtained replacing data given values into equation (5):

Solving we obtain:

Now, inserting (7) , (11), (12) and data given values into equation (2) we have:

Solving we obtain:

Problem # 2

DATA:

SOLUTION

The elastic modulus of cartilage can be obtained using:

Where:

​ is the Tensile Force

is the initial length of cartilage

is the area of cartilage

is the change of length, which is defined as:

Now, we need to obtain the initial length as follows:

Inserting data given values into equation (3) we get:

Solving we obtian:

or , in meters:

Therefore the final lenght can be obtained using:

Inserting (5) into equation (6) we have:

Solving we obtain:

Replacing (5) and (7) into equation (2) we have:

Solving we obtain:

Replacing (5.1) ,(8) and data given values into equation (1) we have:

Solving we obtain: