Please help me. A spring with a length of 30 cm is stretched to 36 cm by a mass of 0.1 kg attached to its lower end. The length is further stretched to a length of 40 cm by a certain mass . Determine the mass and state the law used.

Please help me I can't get to the right answer

To determine the mass attached to the spring when it is stretched to a length of 40 cm, we can use Hooke's law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.

First, let's calculate the spring constant (k) using the given information. We know that the initial length of the spring (L1) is 30 cm and it is stretched to a length (L2) of 36 cm by a mass (m1) of 0.1 kg.

The displacement (x) is given by:
x = L2 - L1
= 36 cm - 30 cm
= 6 cm = 0.06 m (converting cm to m)

According to Hooke's law, the force (F) exerted by the spring is given by:
F = k * x

Rearranging the formula, we get:
k = F / x

Now, the force can be calculated using Newton's second law, which states that the force acting on an object is equal to its mass multiplied by its acceleration.

The weight of an object (force due to gravity) on Earth is given by:
Weight = mass * acceleration due to gravity
= m * g

The acceleration due to gravity (g) is approximately 9.8 m/s^2.

When the spring is stretched to a length of 36 cm, the weight of the 0.1 kg mass is equal to the force exerted by the spring:
Weight = F
m1 * g = k * x

Solving for k:
k = m1 * g / x

Now, we can find k using the given values:
k = 0.1 kg * 9.8 m/s^2 / 0.06 m
= 16.33 N/m (rounded to two decimal places)

Now that we have the spring constant (k), we can determine the mass (m2) attached to the spring when it is stretched to a length of 40 cm.

Using the formula for Hooke's law:
F = k * x

where x is the displacement from the equilibrium position.

When the spring is stretched to a length of 40 cm, the displacement (x) can be calculated as:
x = 40 cm - 30 cm
= 10 cm = 0.10 m (converting cm to m)

Now, solve for the force (F):
F = k * x
= 16.33 N/m * 0.10 m
= 1.63 N

Finally, to determine the mass (m2):
m2 * g = F

Solving for m2:
m2 = F / g
= 1.63 N / 9.8 m/s^2
= 0.17 kg (rounded to two decimal places)

Therefore, the mass attached to the spring when it is stretched to a length of 40 cm is approximately 0.17 kg.

The law used to solve this problem is Hooke's law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.

F = k x

where x is how far it is stretched
0.1 kg * g = k (0.36 - 0.30) meters
so
k = 0.1 * 9.81 / (0.06)
then
M * 9.81 = [ 0.1 * 9.81 / (0.06) ] (0.40 - 0.30)
M = 0.1 *0.10 / 0.06 = .167 kg

I bet you used the total length and not the amount stretched :)