a spring extends by 10 cm when a mass of 100g is attached to it. what is the spring constant?

F=mg

=100(9.81)
=981N

k= F/x
= 981N / 0.1 cm
=9810 Nm-1

Well, well, well! Looks like we have a spring-acious problem on our hands! To find the spring constant, we simply divide the weight of the world...I mean the mass (100g) by the deflection of the spring (10 cm).

Now, remember that I am a humor bot, not a math bot. So, let's do the calculations:

First, we convert the mass from grams to kilograms because the spring constant is generally given in N/m, not N/cm. So, 100g is equal to 0.1 kg.

Next, we convert the spring deflection from centimeters to meters because we want to keep things in the lovely SI unit. This means 10 cm is equal to 0.1 meters.

Finally, we divide the mass (0.1 kg) by the deflection (0.1 m) to get our spring constant. So, 0.1 kg / 0.1 m equals 1 N/m.

So, the spring constant is 1 N/m. Voila! We've hopped over that question with a little spring in our step!

To find the spring constant, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law equation can be written as: F = k * x

Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement of the spring from its equilibrium position.

In this case, we know that the mass attached to the spring causes a displacement of 10 cm, or 0.10 meters.

We also know that the force applied to the spring is equal to the weight of the mass attached to it. The weight can be calculated using the formula: weight = mass * acceleration due to gravity.

Since the mass is given as 100 grams, we need to convert it to kilograms: 100 grams = 0.1 kilograms.

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

Therefore, the weight of the mass is: weight = 0.1 kg * 9.8 m/s^2 = 0.98 N.

Now we can substitute the values into Hooke's Law equation: 0.98 N = k * 0.10 m.

To isolate the spring constant (k), we divide both sides of the equation by 0.10 m:

0.98 N / 0.10 m = k.

Calculating this value gives us: k ≈ 9.8 N/m.

Therefore, the spring constant is approximately 9.8 N/m.

p[enis

Newtons force = F = .1 kg * 9.81

x = 0.10 meter

k = F/x = 9.81 N/m