Question

(10%) Problem 9: $sig.gif?tid=2M68-7D-94-42-ABFD-18791$ When using a pencil eraser, you exert a downward force of 4.5 N at a distance of 2.3 cm from the hardwood-eraser joint. The pencil has a 2.4 mm radius and is held at an angle of 19° to the horizontal. The shear modulus of wood is 1.00 × 1010 N/m2 and the strain modulus is 1.50 × 1010 N/m2. Randomized Variablesf = 4.5 N d = 2.3 cm r = 2.4 mm θ = 19 °

50% Part (a) By how much does the wood flex perpendicular to its length in meters?

50% Part (b) How much is it compressed lengthwise in meters?

Answer 1

A)

Deformation, dL = F cos(theta) Lo/S pi r^2

dL = (4.5 x cos(19) x 0.023)/(10^10 x pi x 0.0024^2)

dL = 5.41 x 10^-7 m

B)

dL = (4.5 x cos(19) x 0.023)/(1.5 x 10^10 x pi x 0.0024^2)

dL = 3.61 x 10^-7 m