Question 1

A sample of tendon 3.00 cm long and 4.00 mm in diameter is found to break under a minimum force of 128 N. If instead the sample had been 1.50 cm long and of uniform composition and cross-sectional area, what minimum force would have been required to break it?

Accepted Answer

The cross-sectional area of the tendon can be calculated as:
A = πr^2 = π(2mm)^2 = 4π mm^2

The stress needed to break the tendon is calculated as:
σ = F/A = 128N / (4π mm^2) ≈ 10.2 N/mm^2

The length of the tendon does not affect the stress required to break it, only the force needed (since stress = force/area). Therefore, the minimum force required to break a 1.50 cm long tendon with the same cross-sectional area and composition would also be 128 N.

Answer: C

Question 2

A copper sphere has a radius of 2.50 m under normal room pressure of 1.0 × 10⁵N/m². If we increase the pressure on this sphere to 10 times the normal room pressure, what is the change in its volume? The bulk modulus for copper is 1.4 × 10¹¹ Pa.

Accepted Answer

The answer of A copper sphere has a radius of...

Question 3

The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 10¹⁰ Pa. What is the sheer stress on the block?

Accepted Answer

Shear stress is given by the product of shear modulus and shear strain. So, shear stress = (3.0 × 10^10 Pa) × (0.0060) = 180 × 10^6 N/m^2.

Question 4

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

Accepted Answer

The answer of A 12-L volume of oil is subjected...

Question 5

A solid steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m². The bulk modulus for this steel is 1.6 × 10¹¹ N/m². What is the change in the radius of the sphere?

Accepted Answer

The change in volume due to pressure can be calculated using the formula for bulk modulus: ΔV/V = -ΔP/B. For a sphere, the change in radius can be derived from the change in volume. Using the given values, the change in radius is approximately -0.062 mm.

Question 6

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place. What is the resulting displacement of the face? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

Accepted Answer

The answer of A shear force of 400 N is...

Question 7

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

Accepted Answer

The answer of A 12-L volume of oil is subjected...

Question 8

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 10⁷ N/m²). By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

Accepted Answer

We can use the formula for bulk modulus:

B = -V(dP/dV)

where B is the bulk modulus, V is the volume, and (dP/dV) is the pressure change per unit volume. Rearranging this formula, we can solve for the change in volume:

-dV/V = dP/B

We can plug in the given values:

dP = 100 atm = 10132500 N/m^2
B = 2.3 × 10^9 N/m^2
dV/V = -10132500/2.3 × 10^9 = -0.004403

So the compression of 1.0 m of water is:

dL = dV = (-0.004403) x (1.0 m) = -0.004403 m = 4.4 x 10^-3 m

Since the volume has decreased, the length has also decreased by the same amount. Thus, the answer is:

Choice C) 4.3 × 10^-3 m

Question 9

When the pressure applied to an unknown liquid is increased from 1.0 × 10⁷ N/m² to 5.5 × 10⁷ N/m², the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid.

Accepted Answer

The answer of When the pressure applied to an unknown...

Question 10

The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 10¹⁰ N/m². What is the displacement of the upper face in the direction of the applied force?

Accepted Answer

The displacement can be calculated using the formula for shear strain: shear strain = displacement / height. Given the shear strain is 0.0060 and the height is 60 cm (or 0.6 m), the displacement is 0.0060 * 0.6 m = 0.0036 m, which is 3.6 mm.

Quiz 10: Equilibrium and Elasticity

A sample of tendon 3.00 cm long and 4.00 mm in diameter is found to break under a minimum force of 128 N. If instead the sample had been 1.50 cm long and of uniform composition and cross-sectional area, what minimum force would have been required to break it?

A copper sphere has a radius of 2.50 m under normal room pressure of 1.0 × 10⁵N/m². If we increase the pressure on this sphere to 10 times the normal room pressure, what is the change in its volume? The bulk modulus for copper is 1.4 × 10¹¹ Pa.

The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 10¹⁰ Pa. What is the sheer stress on the block?

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

A solid steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m². The bulk modulus for this steel is 1.6 × 10¹¹ N/m². What is the change in the radius of the sphere?

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place. What is the resulting displacement of the face? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 10⁷ N/m²) . By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

When the pressure applied to an unknown liquid is increased from 1.0 × 10⁷ N/m² to 5.5 × 10⁷ N/m², the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid.

Quiz 10: Equilibrium and Elasticity

A sample of tendon 3.00 cm long and 4.00 mm in diameter is found to break under a minimum force of 128 N. If instead the sample had been 1.50 cm long and of uniform composition and cross-sectional area, what minimum force would have been required to break it?

A copper sphere has a radius of 2.50 m under normal room pressure of 1.0 × 105 N/m2. If we increase the pressure on this sphere to 10 times the normal room pressure, what is the change in its volume? The bulk modulus for copper is 1.4 × 1011 Pa.

The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 1010 Pa. What is the sheer stress on the block?

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

A solid steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m2. The bulk modulus for this steel is 1.6 × 1011 N/m2. What is the change in the radius of the sphere?

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place. What is the resulting displacement of the face? (The shear modulus for aluminum is 2.5 × 1010 N/m2)

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 107 N/m2) . By how much has 1.0 m3 of water been compressed by this pressure? The bulk modulus of water is 2.3 × 109 N/m2.

When the pressure applied to an unknown liquid is increased from 1.0 × 107 N/m2 to 5.5 × 107 N/m2, the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid.

A copper sphere has a radius of 2.50 m under normal room pressure of 1.0 × 10⁵N/m². If we increase the pressure on this sphere to 10 times the normal room pressure, what is the change in its volume? The bulk modulus for copper is 1.4 × 10¹¹ Pa.

The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 10¹⁰ Pa. What is the sheer stress on the block?

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

A solid steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m². The bulk modulus for this steel is 1.6 × 10¹¹ N/m². What is the change in the radius of the sphere?

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place. What is the resulting displacement of the face? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 10⁷ N/m²) . By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

When the pressure applied to an unknown liquid is increased from 1.0 × 10⁷ N/m² to 5.5 × 10⁷ N/m², the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid.