Question

How much deformation is produced in an aluminum picture nail 1.85mm² in cross-sectional area when a picture weighing 108 N is hung from it? The picture wire rests at the nail head, which is 4.00 mm from the wall.

A. △r= 9.0* 10⁻⁶m
B. △r= 9.0* 10⁻³ m
C. △r= 9.0* 10⁶ m
D. △r= 9.0* 10² m

Answer 1

To calculate the deformation in the aluminum picture nail when a picture is hung from it, you can use Hooke's Law and the formula for strain. The correct answer is B. △r = 9.0 x 10⁻³ m. Option B is correct.

Step-by-step explanation:

To calculate the deformation in the aluminum picture nail when a picture is hung from it, we can use Hooke's Law and the formula for strain.

Step 1: Calculate the force applied on the nail using the weight of the picture:
Force = Weight
Force = 108 N

Step 2: Calculate the stress on the nail:
Stress = Force / Cross-sectional Area
Cross-sectional Area = 1.85 mm² = 1.85 x 10⁻⁶ m²
Stress = 108 N / 1.85 x 10⁻⁶ m²

Step 3: Calculate the deformation using the formula for strain:
Strain = Stress / Young's Modulus
Young's Modulus for aluminum is around 70 GPa = 70 x 10⁹ N/m²
Deformation = Strain x Length
Length = Distance from the nail head to the wall = 4.00 mm = 4.00 x 10⁻³ m
Deformation = (108 N / 1.85 x 10⁻⁶ m²) / (70 x 10⁹ N/m²) x (4.00 x 10⁻³ m)

Step 4: Calculate the final answer:
Deformation = 9.0 x 10⁻³ m

Therefore, the correct option is B. △r = 9.0 x 10⁻³ m.