If a 40 kg brick and a 400 kg brick each dropped from 1 m above a trampoline, find the lowest position of each brick. Assume the trampoline is a simple spring obeying Hooke's law with a k value of 12 000 N/m.

Question

If a 40 kg brick and a 400 kg brick each dropped from 1 m above a trampoline, find the lowest position of each brick. Assume the trampoline is a simple spring obeying Hooke's law with a k value of 12 000 N/m.

I know i must use Fs= kx,
but where do I start?
Do i find Fg at 1 m?

Answer 1

I would do it with energy.

mg(h+x)=1/2 k x^2
then solve for x in each case.

Answer 2

okay, but what is the start of that eq'n?

It looks similar to Eg=Ek ?

Answer 3

PEintrampoline=PE gravity lost

Answer 4

pe= potential energy?

Answer 5

and how do i solve for x when it is on oth sides of the eq'n?

Answer 6

multiply it all out, you will get a quadratic equation. Use the quadratic formula.

Answer 7

To find the lowest position of each brick on the trampoline, you need to consider two main forces acting on each brick: the gravitational force (Fg) and the spring force (Fs).

To start, you are correct in using Hooke's law to find the spring force. Hooke's law states that Fs = kx, where Fs is the spring force, k is the spring constant, and x is the displacement from the equilibrium position.

However, before you can find the spring force, you first need to calculate the gravitational force acting on each brick at a height of 1 m. The gravitational force can be calculated using the formula Fg = mg, where Fg is the gravitational force, m is the mass of the brick, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Let's calculate the gravitational force for each brick:
For the 40 kg brick:
Fg = (40 kg) * (9.8 m/s^2) = 392 N

For the 400 kg brick:
Fg = (400 kg) * (9.8 m/s^2) = 3920 N

Now that we have calculated the gravitational forces, we can find the spring forces acting on each brick. We will assume that the lowest position corresponds to the maximum displacement of the spring from its equilibrium position.

Using Hooke's law (Fs = kx), we can set the spring force equal to the gravitational force and solve for x:
Fs = kx

For the 40 kg brick:
392 N = (12,000 N/m) * x
x = 392 N / (12,000 N/m) = 0.0327 m (approximately)

For the 400 kg brick:
3920 N = (12,000 N/m) * x
x = 3920 N / (12,000 N/m) = 0.3267 m (approximately)

So, the lowest position for the 40 kg brick would be at a displacement of approximately 0.0327 m from the equilibrium position, and the lowest position for the 400 kg brick would be at a displacement of approximately 0.3267 m from the equilibrium position.