A spring scale being used to measure the weight of an object reads 12.8 N when it is used on earth. The spring stretches 4.95 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.
To find the reading of the spring scale on the moon, we need to use the relationship between weight, mass, and gravitational acceleration. On Earth, the weight of an object is given by the formula:
Weight = mass * gravitational acceleration on Earth (g on Earth) ----- (1)
On the moon, where the gravitational acceleration is 1/6 times that of Earth, the weight of the same object can be found using the formula:
Weight on Moon = mass * gravitational acceleration on Moon (g on Moon) ----- (2)
Now, we can use the given information to solve for the reading of the spring scale on the moon.
Given: Weight on Earth (W on Earth) = 12.8 N
Weight on Moon (W on Moon) = ?
From equation (1):
W on Earth = mass * g on Earth
From equation (2):
W on Moon = mass * g on Moon
To find the reading of the spring scale on the moon, we can set up a proportion:
W on Earth / W on Moon = g on Earth / g on Moon
Substituting the given values:
12.8 / W on Moon = g on Earth / (1/6 * g on Earth)
Simplifying the expression:
12.8 / W on Moon = 6/1
Cross-multiplying:
6 * W on Moon = 12.8 * 1
Solving for W on Moon:
W on Moon = (12.8 * 1) / 6
Calculating the value:
W on Moon = 2.13 N
Therefore, the reading of the spring scale on the moon is 2.13 N.
To find the period for vertical oscillations of the spring on the moon, we can use Hooke's Law and the formula for the period of a mass-spring system.
Hooke's Law states that the force exerted by a spring is directly proportional to its displacement.
On Earth, the force exerted by the spring can be given by the formula:
Force on Earth (F on Earth) = k * displacement ----- (3)
On the moon, where the gravitational acceleration is 1/6 times that of Earth, the force exerted by the spring can be given by the formula:
Force on Moon (F on Moon) = k * displacement ----- (4)
Now, the period of a mass-spring system can be found using the formula:
Period T = 2π * √(m / k)
Where m is the mass of the object and k is the spring constant.
Given: Displacement = 4.95 cm = 0.0495 m
From equation (3):
F on Earth = k * displacement
From equation (4):
F on Moon = k * displacement
Since the displacement and spring constant are the same in both cases, the force exerted by the spring on the moon will be the same as on Earth.
Therefore, the period of vertical oscillations of the spring on the moon will be the same as on Earth.
Hence, the period for vertical oscillations of the spring on the moon will be the same as it is on Earth.