Question

In this example we will use pendulum motion to actually measure the acceleration of gravity on a different planet. An astronaut on the surface of Mars measures the frequency of oscillation of a simple pendulum consisting of a ball on the end of a string. He finds that the pendulum oscillates with a period of 1.5 s. But the acceleration due to gravity on Mars is less than that on earth, gMars=0.38gearth. Later, during a journey to another planet, the astronaut finds that his simple pendulum oscillates with a period of 0.92 s. What planet is he now on?

Answer 1

To find out what planet the astronaut is on, we can use the length and period of the pendulum to calculate the unknown planet's acceleration due to gravity using the formula for the period of a simple pendulum. By comparing the equations for Mars and the unknown planet, we can find the unknown acceleration due to gravity.

Step-by-step explanation:

To identify the planet the astronaut is on, we can use the formula for the period of a simple pendulum:

T = 2π √(L / g)

Where T is the period, L is the length of the string, and g is the acceleration due to gravity.

We know that the period on Mars is 1.5 s and the acceleration due to gravity on Mars is 0.38 times that of Earth, so we can set up the following equation:

1.5 s = 2π √(L / (0.38g_earth))

Similarly, for the unknown planet, the period is 0.92 s, so we have:

0.92 s = 2π √(L / g_unknown)

To find the unknown planet, we can compare the two equations:

1.5 s / (0.92 s) = (√(L / (0.38g_earth))) / (√(L / g_unknown))

Simplifying the equation:

(√(L / g_unknown)) = (1.5 s / (0.92 s)) * (√(0.38g_earth))

Squaring both sides of the equation:

L / g_unknown = ((1.5 s / (0.92 s)) * (√(0.38g_earth)))^2

Finally, solving for g_unknown:

g_unknown = L / (((1.5 s / (0.92 s)) * (√(0.38g_earth)))^2)

Using the given data, we can substitute the values and calculate g_unknown.