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 1/6g

Find the reading of the spring scale on the moon.


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

CAN YOU PLEASE PROVIDE THE ANSWER WITH WORK? THANK YOU VERY MUCH

if the force on the moon is 1/6 of that than Earth, the readin gwill be 1/6.

Period? Period=2PI sqrt (mass/k)

but k= 17.1/.0440 N/m, mass is 17.1/9.8 kg

Sure! Let's solve each part of the problem step-by-step.

1. Finding the reading of the spring scale on the moon:

Given:
Weight on Earth (W1) = 17.1 N
Elongation on Earth (Δx1) = 4.40 cm

We can use Hooke's Law to find the spring constant (k) using the equation:

W1 = k * Δx1

Substituting the values:

17.1 N = k * 0.044 m (since 1 cm = 0.01 m)

Now we need to find the weight on the moon (W2).

Weight on the moon (W2) = Mass (m) * Acceleration due to gravity on the moon (g2)

Given:
Acceleration due to gravity on the moon (g2) = 1/6g
(where g is the acceleration due to gravity on Earth. g = 9.8 m/s²)

So, g2 = (1/6) * (9.8 m/s²)

Now, W2 = m * g2

But W2 = k * Δx2
(where Δx2 is the elongation on the moon)

Since W1 = W2 (weight is the same), we can write:

k * Δx1 = k * Δx2

From this equation, we can find the elongation on the moon (Δx2):

Δx2 = Δx1

Now, substituting the values into Hooke's Law:

k * Δx2 = 17.1 N (since W1 = W2)

k * Δx1 = 17.1 N

k * 0.044 m = 17.1 N

k = 17.1 N / 0.044 m

Calculate the value of k using a calculator:

k ≈ 388.64 N/m

Now, to find the reading of the spring scale on the moon, we can use Hooke's Law:

W2 = k * Δx2

W2 = 388.64 N/m * 0.044 m

Calculate the value using a calculator:

W2 ≈ 17.06 N

Therefore, the reading of the spring scale on the moon is approximately 17.06 N.

2. Finding the period for vertical oscillations of the spring on the moon:

The period (T) of vertical oscillations for a mass-spring system can be calculated using the equation:

T = 2π * √(m / k)

Given:
Mass (m) is not provided.

Since the mass is not provided, we cannot determine the period of oscillations accurately without it. The period depends on the mass.

However, if you have the mass provided, you can substitute the values into the equation and calculate the period using a calculator.

I hope this helps! Let me know if you have any further questions.

To find the reading of the spring scale on the moon, we can use the following equation:

F = kx

where F is the force applied to the spring (weight), k is the spring constant, and x is the displacement of the spring.

On Earth, the weight of the object is given as 17.1 N. Since the gravitational acceleration on the moon is 1/6th of that on Earth, we can find the weight of the object on the moon using the equation:

Weight on the Moon = (1/6) * Weight on Earth

Weight on the Moon = (1/6) * 17.1 N = 2.85 N

Now we need to find the spring constant, k. We can use the information that the spring stretches 4.40 cm under the load. We need to convert this displacement to meters:

Displacement, x = 4.40 cm = 0.044 m

Now we can rearrange the equation F = kx to solve for k:

k = F / x

k = 17.1 N / 0.044 m = 388.64 N/m

Finally, we can use the spring constant and the weight on the moon to find the reading of the spring scale:

F = kx

Reading of the Spring Scale on the Moon = k * x = 388.64 N/m * 0.044 m ≈ 17.08 N

Therefore, the reading of the spring scale on the moon is approximately 17.08 N.

To find the period for vertical oscillations of the spring on the moon, we can use the equation:

T = 2π √(m/k)

where T is the period, π is a mathematical constant (approximately 3.14), m is the mass of the object, and k is the spring constant.

Since the mass of the object is not provided, we cannot determine the period without additional information.

Please note that the above calculations assume that the spring obeys Hooke's Law and that there are no other external factors affecting the results.