A spring scale being used to measure the weight of an object reads 17.1 N when it is used on earth. The spring stretches 4.40 cm under the load. The same object is weighed on the moon, where gravitational acceleration is

1
6
g.

Find the reading of the spring scale on the moon.

HELP PLEASE

mg=17.1 N =>

mg= kx
k=mg/x
On the moon
mg`=kx₁
x₁=mg`/k =m•1.6•g•x /mg=1.6x=1.6•0.044=0.0704 m

To find the reading of the spring scale on the moon, we need to determine the weight of the object on the moon and then find the corresponding spring scale reading.

Step 1: Calculate the weight of the object on the moon.
On the moon, the gravitational acceleration is 1/6th of the acceleration due to gravity on Earth (approximated as ~9.8 m/s^2). Therefore, the gravitational acceleration on the moon (g_moon) can be calculated as:

g_moon = (1/6) * g_earth

Where g_earth = 9.8 m/s^2.

Substituting the value of g_earth, we get:

g_moon = (1/6) * 9.8 ≈ 1.63 m/s^2

The weight of an object on the moon (W_moon) can be calculated using the formula:

W_moon = m * g_moon

Where m represents the mass of the object.

Step 2: Find the spring scale reading on the moon.
To determine the spring scale reading on the moon, we need to use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring.

F = k * x

Where F is the force exerted by the spring (spring scale reading), k is the spring constant, and x is the displacement of the spring.

We can assume that the spring constant k remains the same on the moon as it is on Earth.

Therefore, we can set up a proportion to relate the spring scale reading on the moon (F_moon) and the displacement of the spring (x_moon) to the known values on Earth (F_earth = 17.1 N and x_earth = 4.40 cm).

F_moon / x_moon = F_earth / x_earth

Substituting the known values:

F_moon / x_moon = 17.1 N / 4.40 cm

Step 3: Solve for F_moon.
Rearranging the equation, we get:

F_moon = (F_earth / x_earth) * x_moon

Substituting the known values:

F_moon = (17.1 N / 4.40 cm) * x_moon

Remember to convert the displacement to meters before substituting it in the equation.

Step 4: Calculate the spring scale reading on the moon.
Now you can calculate the spring scale reading on the moon using the value of F_moon obtained in the previous step.

Just plug in the known values and solve:

F_moon = (17.1 N / 4.40 cm) * x_moon

Make sure to convert the displacement back to centimeters for the final answer.

I hope this explanation helps you solve the problem!