Question

Consult Interactive Solution 16.15 in order to review a model for solving this problem. To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.123-kg ball from the end of a wire. The wire has a length of 1.52 m and a linear density of 4.41 × 10-4 kg/m. Using electronic equipment, the astronaut measures the time for a transverse pulse to travel the length of the wire and obtains a value of 0.0833 s. The mass of the wire is negligible compared to the mass of the ball. Determine the acceleration due to gravity.

Answer 1

Answer:

 g = 1.19 m / s²

Explanation:

Let's solve this problem in parts.

Let's start by looking for the speed of the pulse in the wire, the wave speed is constant

          v = l / t

let's calculate

          v = 1.52 / 0.0833

           v = 18.25 m / s

now we can use the relationship between velocity and material properties

           v = $\sqrt{\frac{T}{\mu } }$

           T = v² μ

let's calculate

           T = 18.25² 4.41 10-4

           T = 1.4688 10-1 N

finally let's use the equilibrium condition

            T - W = 0

            W = T

             m g = T

             g = T / m

we calculate

              g = 1.4688 10⁻¹ / 0.123

              g = 1.19 m / s²