A 1.2-kg piece of cheese is placed on a vertical spring of negligible mass and a force constant 1800 N/m. What is the length of compression of the spring?

weight = m g = 1.2 * 9.8 N

deflection = 1.2*9.8/1800 meters

Well, if we're talking about cheese and springs, I'm all ears! Let's have some cheesy fun with this physics problem!

The length of compression of the spring can be found using Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement (or compression).

So, F = kx, where F is the force, k is the force constant, and x is the displacement.

In this case, the force is the weight of the cheese, which is given by F = mg, where m is the mass of the cheese and g is the acceleration due to gravity.

Now, we know the mass of the cheese is 1.2 kg, and the acceleration due to gravity is approximately 9.8 m/s².

So, F = (1.2 kg)(9.8 m/s²), which gives us the force exerted by the cheese on the spring.

Plugging this value into Hooke's Law, we get (1800 N/m)(x) = (1.2 kg)(9.8 m/s²).

Simplifying this equation, we find x = (1.2 kg)(9.8 m/s²)/(1800 N/m).

Calculating this, we get x ≈ 0.067 m.

So, the length of compression of the spring is approximately 0.067 meters. That's quite a stretch for a little piece of cheese, don't you think?

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

Hooke's Law can be expressed as:

F = -kx

Where:
F is the force exerted by the spring (in Newtons),
k is the force constant of the spring (in N/m), and
x is the displacement from the equilibrium position (in meters).

In this case, the weight of the cheese is the force exerted by the spring. The weight is given by:

F = m * g

Where:
m is the mass of the cheese (in kg), and
g is the acceleration due to gravity (9.8 m/s^2).

Substituting the values given, we have:

F = (1.2 kg) * (9.8 m/s^2) = 11.76 N

Now, we can use Hooke's Law to find the displacement (compression) of the spring:

11.76 N = - (1800 N/m) * x

To solve for x, we isolate it:

x = - (11.76 N) / (1800 N/m)

Calculating this gives us:

x ≈ -0.006533 m

So, the length of compression of the spring is approximately 0.006533 meters.

To find the length of compression of the spring, we can 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.

The formula for Hooke's Law is:

F = -kx

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

In this case, the weight of the cheese acts as the force exerted on the spring. Since the cheese is placed vertically, we need to calculate the weight using the formula:

Weight = mass * acceleration due to gravity

Given that the mass of the cheese is 1.2 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:

Weight = 1.2 kg * 9.8 m/s^2 = 11.76 N

Now, we can equate the force exerted by the spring to the weight:

-kx = Weight

Substituting the values:

-1800 N/m * x = 11.76 N

Solving for x:

x = -11.76 N / -1800 N/m

x ≈ 0.00653 m

Therefore, the length of compression of the spring is approximately 0.00653 meters.