Help with calcuating force constant ?

[nukeman]

Homework Statement

A 320 kg wooden raft floats on a lake in equilibrium. When a 75 kg man steps carefully onto the raft, it floats 3.5 cm deeper into the water. When he steps off, the raft oscillates for a while.

(a) The buoyant force of the water on the raft is a restoring force that is directly proportional to how deep the raft sits in the water. In this way, the water acts like a mechanical spring. Calculate the force constant of this spring.

Homework Equations

The Attempt at a Solution

I am not sure how to get the force constant out of this, as if it were a spring.

k = f/displacement ?

 

[Curious3141]

Homework Statement

A 320 kg wooden raft floats on a lake in equilibrium. When a 75 kg man steps carefully onto the raft, it floats 3.5 cm deeper into the water. When he steps off, the raft oscillates for a while.

(a) The buoyant force of the water on the raft is a restoring force that is directly proportional to how deep the raft sits in the water. In this way, the water acts like a mechanical spring. Calculate the force constant of this spring.

Homework Equations

The Attempt at a Solution

I am not sure how to get the force constant out of this, as if it were a spring.

k = f/displacement ?

So what is the force the man exerts on the raft (and hence the water) by stepping onto it? This is exactly balanced by the buoyant force. Express this in N (Newton).

And what is the displacement of the raft in the water caused by that force? Express this in m (metre).

After you work out what those two are, just divide as per the equation you quoted. The units are $Nm^{-1}$

 

[nukeman]

so, 75kg * 9.8 = 735 J

So,

735j = (x)(0.035) solve for x gives me 21,000 NM

is that correct?

 

[Curious3141]

so, 75kg * 9.8 = 735 J

So,

735j = (x)(0.035) solve for x gives me 21,000 NM

is that correct?

Why J (Joule) as the unit for force? Remember, weight = mg, and this is a force measured in Newton. Potential energy due to Earth's gravitation = mgh, and this is energy measured in Joule. Big difference.

So the weight of the man is mg = 75*9.8 = 735N (Newton).

The displacement x is 3.5cm = 3.5/100m = 0.035m.

Hence the force constant k = F/x = 735/0.035 = 21000N/m (Newton-per-metre, not the slash signifying division between Newton and metre. Instead of the slash one can also write $Nm^{-1}$ (and many modern texts prefer this notation). This is NOT the same as Nm (Newton-metre, obtained by multiplying Newton and metre, and which is a unit of energy equivalent to Joule).

Please be careful with your units. Wrong unit = wrong answer. Other than that, your figures are fine.