Finding a spring constant of a car

[ChickysPusss]

Homework Statement

A car has a total mass of 2000kg, and a ground clearance of 40cm. But some fat dude got in and he made the ground clearance 30cm. What is the spring constant for this bad boy of a car? (The dude was so fat he made the shocks act like springs if you can believe it.) Also, it's a fact that the natural frequency of said springs are .6667 HZ.

Homework Equations

F = -kx

The Attempt at a Solution

So I tried being like: (2000kg)*(9.8m/s^2) = -kx
and then I was like: (2000kg + Xkg) * (9.8m/s^2) = -k(x-.1m)

I tried solving for k as hard as I could cause I really want it, but there are too many variables and I can't figure out what to do. My physics teacher says he wants me to fail and I'd like to show him that I'm not a total turd. Thank you.

 

[Simon Bridge]

The car weight compresses the springs to 40cm, but it is the car+dude that compresses the springs to 30cm. So the extra weight of the dude compresses the springs an extra how much?

Your trouble is that you don't know the weight of the dude or the spring constant ... that's two unknowns: so you need two equations.

You also need the equation for the natural frequency of a mass on a spring.

 

[ChickysPusss]

Ok Physics bros... I think I had a stroke of genius, thanks to Simon Bridge, but I'm wondering of the mathematical/physical legality of what I've done.

So...

(2000kg)*(9.8m/s^2) = -kx = (2000kg)*(g) = -kx

(2000kg + Xkg) * (9.8m/s^2) = -k(x-.1m)= (2000kg +Xkg) * (g)

Is it legal to do this...

(-k(x-.1m)= (2000kg +Xkg) * (g)) - (-kx = (2000kg)*(g)) = (X*g = -.1k)

Then say that k = -(X*g)/.1

Cause if that's k, I can plug it into other formula and I'm good to go.

 

[Simon Bridge]

Are you confusing the clearance with the compression?

Let the uncompressed clearance be x₀ - then the car weight Mg compresses the springs by x, giving a clearance of 40cm ... eg.

40cm = x₀-x: kx=Mg ... thus: 40cm = x₀-Mg/k

similarly for Car + dude: 30cm = x₀-(M+m)g/k

But you don't know x₀, m, or k ... so that's two equations and three unknowns.

You are still missing the equation for the natural frequency of the spring.

 

[Nickie]

First of all, I want to commend you for your efforts in trying to solve this problem. As a scientist, it is important to persevere and keep trying even when faced with challenges.

In order to find the spring constant of the car, we need to use the equation F = -kx, where F is the force applied by the spring, k is the spring constant, and x is the displacement from the equilibrium position. In this case, the displacement is the difference between the original ground clearance (40cm) and the new ground clearance (30cm), which is 0.1m.

We also need to consider the weight of the car and the person inside. When the ground clearance was 40cm, the total weight of the car was 2000kg * 9.8m/s^2 = 19,600N. When the ground clearance was reduced to 30cm, the total weight of the car and the person was (2000kg + Xkg) * 9.8m/s^2 = (2000 + X) * 9.8N.

Using the equation F = -kx, we can set up the following equation:

(2000 + X) * 9.8N = -k * 0.1m

Solving for k, we get:

k = (2000 + X) * 9.8N / 0.1m

However, we still have the variable X, which represents the weight of the person. Without knowing the exact weight of the person, we cannot solve for the spring constant. We would need more information in order to find the value of X and ultimately, the spring constant of the car.

I understand that you want to prove your physics teacher wrong, but it is important to remember that science is about finding answers based on evidence and data. If we do not have all the necessary information, we cannot come to a conclusive solution. Keep up the good work and continue to ask questions and seek understanding.