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 mass suspended from it. Assume that the wire has a mass of 4.10 g and a length of 1.60 m and that a 3.00 kg mass is suspended from it. A pulse requires 64.3 ms to traverse the length of the wire. Calculate the local g from these data. (You may neglect the mass of the wire when calculating the tension in it.)

? m/s2

Get the wave speed from the ratio

(wire length)/64.3*10^-3 s

The wave speed equals the square root of (Wire tension)/(wire lineal density)

Solve for the wire tension, T. That will equal the weight (in Newtons) of the 3 kg mass, from which you can derive g on that planet.

To calculate the local value of gravitational acceleration (g), we can use the formula:

g = 4π²L / T²

where:
- π is approximately 3.14159 (you can use the value on your calculator)
- L is the length of the wire
- T is the time taken for the pulse to traverse the wire

In this scenario:
- L = 1.60 m (given)
- T = 64.3 ms = 0.0643 s (given)

Plugging these values into the formula:

g = 4π²(1.60) / (0.0643)²

Now we can calculate g:

To calculate the local value of g, we can use the following formula:

g = L / T^2

where L is the length of the wire and T is the time it takes for a pulse to travel down the wire.

From the given data, we have:
L = 1.60 m
T = 64.3 ms = 0.0643 s

Now, substitute these values into the formula to calculate g:

g = 1.60 m / (0.0643 s)^2

First, calculate (0.0643 s)^2:
(0.0643 s)^2 = 0.00413349 s^2

Now, calculate g:
g = 1.60 m / 0.00413349 s^2

Divide 1.60 m by 0.00413349 s^2:
g ≈ 387.52 m/s^2

Therefore, the local value of g on the small planet is approximately 387.52 m/s^2.