A 25-kg television set rests on four rubber pads, each one having a height of 1.0 cm and a radius of 0.60 cm. A 200-N horizontal force is applied to the television set. How far does it move sideways due to the deformation of the rubber pads if the pads do not slide on the floor? The shear modulus of these rubber pads is $2.6 \times 10 ^ { 6 } \mathrm {~Pa}$
A) 1.3 mm
B) 6.8 mm
C) 3.4 mm
D) 1.7 mm
E) 1.5 mm

Question

A 25-kg television set rests on four rubber pads, each one having a height of  1.0 cm and a radius of  0.60 cm. A  200-N horizontal force is applied to the television set. How far does it move sideways due to the deformation of the rubber pads if the pads do not slide on the floor? The shear modulus of these rubber pads is $2.6 \times 10 ^ { 6 } \mathrm {~Pa}$
A)  1.3 mm
B)  6.8 mm
C)  3.4 mm
D) 1.7 mm
E)  1.5 mm

Quizplus · Accepted Answer

The deformation ($x$) due to the shear stress can be calculated using the formula for shear deformation: $x = \frac{F \cdot h}{A \cdot G}$, where $F$ is the force applied, $h$ is the height of the rubber pads, $A$ is the cross-sectional area of the pads, and $G$ is the shear modulus. Given that the force is 200 N, the height of the pads is 1.0 cm (or 0.01 m), the radius of each pad is 0.60 cm (or 0.006 m), and the shear modulus is $2.6 \times 10^6$ Pa, the cross-sectional area of one pad is $\pi r^2 = \pi (0.006)^2$ m$^2$. Since there are four pads, the total area is $4 \times \pi (0.006)^2$ m$^2$. Plugging these values into the formula gives the deformation, which, when calculated correctly, results in approximately 1.7 mm.

A 25-Kg Television Set Rests on Four Rubber Pads, Each 2.6×106 Pa2.6 \times 10 ^ { 6 } \mathrm {~Pa}2.6×106 Pa

A 25-Kg Television Set Rests on Four Rubber Pads, Each $2.6 \times 10 ^ { 6 } \mathrm {~Pa}$