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 !!!
To find the reading of the spring scale on the moon, we need to determine the weight of the object on the moon. We have the weight on Earth given as 17.1 N.
Step 1: Determine the weight on the moon.
The weight of an object is given by the equation:
Weight = mass x acceleration due to gravity
On Earth, the acceleration due to gravity is approximately 9.8 m/s^2. On the moon, where the gravitational acceleration is 1/6 of Earth's, the acceleration due to gravity would be:
Acceleration on moon = (1/6) x 9.8 m/s^2 = 1.633 m/s^2
Step 2: Calculate the mass of the object.
We can rearrange the equation to solve for mass:
Weight = mass x acceleration due to gravity
17.1 N = mass x 9.8 m/s^2
mass = 17.1 N / 9.8 m/s^2 = 1.745 kg (approximately)
Step 3: Calculate the weight on the moon.
Weight on moon = mass x acceleration on moon
Weight on moon = 1.745 kg x 1.633 m/s^2 = 2.85 N (approximately)
Therefore, the reading of the spring scale on the moon would be approximately 2.85 N.
To find the period for vertical oscillations of the spring on the moon, we can use the formula for the period of a mass-spring system:
T = 2π√(m/k)
where T is the period, m is the mass, and k is the spring constant.
Step 1: Determine the spring constant.
The spring constant can be calculated using Hooke's Law:
F = kx
where F is the force applied to the spring, k is the spring constant, and x is the displacement.
Given that the spring stretches 4.40 cm (which is equivalent to 0.044 m) under the load of 17.1 N, we can rearrange the equation to solve for the spring constant:
k = F / x = 17.1 N / 0.044 m = 388.64 N/m (approximately)
Step 2: Calculate the period.
The mass of the object is already known to be 1.745 kg.
T = 2π√(m/k) = 2π√(1.745 kg / 388.64 N/m)
Using a calculator, we find that the period would be approximately 0.316 s.
Therefore, the period for vertical oscillations of the spring on the moon would be approximately 0.316 seconds.
To find the reading of the spring scale on the moon, we need to consider the difference in gravitational acceleration between the Earth and the Moon.
On Earth, the gravitational acceleration is approximately 9.8 m/s^2. On the Moon, the gravitational acceleration is approximately 1/6th (1/6g) of the Earth's gravitational acceleration.
Let's solve for the reading of the spring scale on the moon:
1. First, we need to find the weight of the object on the moon using the given weight on Earth.
Weight (on Earth) = 17.1 N
2. Now, we can find the weight (W) of the object on the moon using the relation between weight and gravitational acceleration:
W = mg
where m is the object's mass and g is the acceleration due to gravity.
On the Moon, the gravitational acceleration is 1/6g, so we have:
W (on Moon) = (1/6g) × m
3. Next, we need to find the mass of the object. We can rearrange the weight formula to solve for mass:
m = W / g (on Earth)
Substituting the given values:
m = 17.1 N / 9.8 m/s^2
Calculate this to find the mass of the object.
4. Now, substitute the mass into the formula derived in step 2 to find the weight on the Moon:
W (on Moon) = (1/6g) × (mass)
Calculate this to find the weight of the object on the Moon.
Finally, the reading on the spring scale on the Moon will be equal to the weight of the object on the Moon.
To find the period for vertical oscillations of the spring on the Moon, we need to consider Hooke's Law and the relationship between the period and the spring constant.
The period (T) of a mass-spring system is given by:
T = 2π√(m/k)
where m is the mass attached to the spring and k is the spring constant.
1. We have already determined the mass of the object in the previous calculations.
2. The spring constant (k) can be calculated using Hooke's Law:
k = F / x
where F is the force applied to the spring (weight) and x is the displacement or stretch of the spring.
In this case, F is the weight of the object on the Moon and x is the stretch of the spring.
3. Calculate the spring constant (k) using the formula above.
4. Substitute the values of mass (m) and spring constant (k) into the formula for the period (T) and calculate the period for vertical oscillations of the spring on the Moon.
Remember to use correct units throughout the calculations.
I hope this explanation helps you understand the problem and the steps involved in finding the solutions. Let me know if you have any further questions!