Question

On Earth, a spring stretches by 5.0 cm when a mass of 3.0 kg is suspended from one end.

Answer 1

Answer:

Mass = 18.0 kg

Explanation:

From Hooke's law,

F = ke

where: F is the force, k is the spring constant and e is the extension.

But, F = mg

So that,

mg = ke

On the Earth, let the gravitational force be 10 m/$s^{2}$.

3.0 x 10 = k x 5.0

30 = 5k

⇒ k = $\frac{30}{5}$ ................ 1

On the Moon, the gravitational force is $\frac{1}{6}$ of that on the Earth.

m x $\frac{10}{6}$ = k x 5.0

$\frac{10m}{6}$ = 5k

⇒ k = $\frac{10m}{30}$ ............. 2

Equating 1 and 2, we have;

$\frac{30}{5}$  = $\frac{10m}{30}$

m = $\frac{900}{50}$

    = 18.0

m = 18.0 kg

The mass required to produce the same extension on the Moon is 18 kg.

Answer 2

Answer:

18 kg

Explanation:

• weight (N) = mass (kg) × gravitational acceleration (m/s²)
• force (N) = k (spring constant) × extension (m)

On Earth, acceleration of gravity is 10 m/s²

• weight = 3.0 (kg) × 10 (m/s²)

• weight = 30 (N)

Since weight is a force, the force is 30 N. The value of spring constant is unknown

• 30 (N) = k × 5 (m)
• k = 6 (m/N)

Spring constant is 6. Now let's find the mass on the Moon

• mass (kg) × gravitational acceleration (m/s²) = k (spring constant) × extension (m)

Gravitational acceleration of the moon is 1/6 of that on Earth. Earth's g = 10, so Moon's g = 10/6

• m × 10/6 = 6 × 5
• m = 30/(10/6)
• m = 18

The mass is 18 kg