Question

An astronaut on a small planet wishes to measure the local value of g by timing pulses traveling down a wire which has a large object suspended from it. Assume a wire of mass 4.10 g is 1.60 m long and has a 3.00-kg object suspended from it. A pulse requires 39.2 ms to traverse the length of the wire. Calculate g_planet from this data. (You may neglect the mass of the wire when calculating the tension in it.)

Answer 1

Find gravity due to acceleration on small planet, using below method:

We know wave speed on a string is given by:

V = sqrt (T/)

Also V = length of string/time taken = L/t = 1.60 m/(39.2*10^-3) sec

T = tension in string = m*g

m = mass of object attached on string = 3.00 kg

g = acceleration due to gravity on planet = ? m/s^2

= linear mass density of string = mass per unit length = m0/L = 4.10*10^-3/1.60

So,

V = L/t = sqrt (m*g/(m0/L))

g = m0*L/(m*t^2)

g = 4.10*10^-3*1.60/(3.00*(39.2*10^-3)^2)

g = 1.42 m/s^2

Let me know if you've any query.