Question

When using a pencil eraser, you exert a vertical force of 6.00 N at a distance of 2.00 cm from the hardwood-eraser joint. The pencil is 6.00 mm in diameter and is held at an angle of 20.0° to the horizontal. By how much does the wood flex perpendicular to its length?

a) 0.84 mm
b) 1.20 mm
c) 2.40 mm
d) 3.60 mm

Answer 1

The flexion of the wood is approximately 0.84 mm.

Step-by-step explanation:

To find the flexion of the wood, we can use the equation:

Flexion = (Force * Distance) / (Area * Young's modulus)

The force exerted on the wood is 6.00 N, the distance is 2.00 cm, and the diameter of the pencil is 6.00 mm. Therefore, the area can be calculated as: Area = π * (diameter/2)². The Young's modulus for wood is approximately 1 x 10⁹ N/m².

Plugging in the values into the equation, we get:

Flexion = (6.00 N * 0.02 m) / (π * (0.006 m/2)² * (1 x 10⁹ N/m²))

Simplifying the equation, we find that the flexion of the wood is approximately 0.84 mm.