Question

The drawing shows two crates that are connected by a steel wire that passes over a pulley. The unstretched length of the wire is 1.70 m, and its cross-sectional area is 1.25 10-5 m2. The pulley is frictionless and massless. When the crates are accelerating, determine the change in length of the wire. Ignore the mass of the wire.

Answer 1

Answer:  The change in length of the wire is= 8.613*10⁻⁷ m

Explanation:

                        The formula for Young's Modulus = Stress/ Strain

                                                    $Y= \frac{F/A}{x/L} =\frac{F*L}{A*x}$   where x represents the change in length.

Rearranging the equation and making F/A the subject of the formula gives us            

                                                         $\frac{F}{A} = Y* \frac{x}{L}$

The use of area is not required as we have assumed the the force of Atmosphere is being applied on the crates which means

                                                    F/A = Atmospheric Pressure

                                                    1 atm = 101325 Pa

now solve:

                                                     101325 = (2.10*10¹¹ Pa) * (x/1.7)

Therefore, x= 8.613*10⁻⁷ m