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.

Find the period for vertical oscillations of the spring on the moon.

This question has been really bugging me! Can someone please provide the work and answer so I can work backwards to learn this!? THANK YOU VERY MUCH FOR YOUR TIME !!!

Wt = (1/6) *17.1 = 2,85 N.

To find the reading of the spring scale on the moon, we can start by understanding the relationship between weight, gravitational acceleration, and the reading of the spring scale.

The weight of an object is given by the formula:

Weight = mass * gravitational acceleration

On Earth, the gravitational acceleration is approximately 9.8 m/s^2. On the Moon, the gravitational acceleration is 1/6 times that of Earth's, so it is:

Gravitational acceleration on the Moon = (1/6) * 9.8 m/s^2 = 1.63 m/s^2

Now, let's find the mass of the object. We can use the formula for weight to rearrange and solve for mass:

mass = Weight / gravitational acceleration

On Earth:
mass = 17.1 N / 9.8 m/s^2 = 1.745 kg

Now, we can find the reading of the spring scale on the Moon using the formula for weight:

Weight on the Moon = mass * gravitational acceleration on the Moon

Weight on the Moon = 1.745 kg * 1.63 m/s^2 = 2.84135 N

Therefore, the reading of the spring scale on the Moon is approximately 2.84 N.

Moving on to the second part of your question: finding the period for vertical oscillations of the spring on the Moon.

The period of oscillation of a spring can be calculated using the formula:

Period = 2π * √(mass / spring constant)

The mass of the object is still 1.745 kg, as calculated earlier.

The spring constant (k) can be determined using Hooke's Law:

Force = -k * displacement

Given that the spring stretches 4.40 cm under the load, we can convert this to meters by dividing by 100:

Displacement = 4.40 cm / 100 = 0.044 m

Since the formula for weight is:

Weight = k * displacement

We can rearrange this formula to solve for the spring constant:

k = Weight / displacement = 17.1 N / 0.044 m = 388.6364 N/m

Now we can calculate the period using the formula:

Period = 2π * √(mass / spring constant) = 2π * √(1.745 kg / 388.6364 N/m)

Period ≈ 1.1754 seconds

Therefore, the period for vertical oscillations of the spring on the Moon is approximately 1.18 seconds.

I hope this explanation helps you understand how to approach and solve these problems. If you have any further questions, feel free to ask!