Question

# An astronaut on a small planet wishes to measure the local value of g by timing...

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 gplanet from this data. (You may neglect the mass of the wire when calculating the tension in it.)

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.