Experimental problem. Help would be appreciated?

Question

In the laboratory you are given a cylindrical beaker containing a fluid and you are asked to determine the density of the fluid. You are to use a negligible mass and unknown spring constant attacked to a stand An Irregularly shaped object of known mass and density hangs from the spring. You may also choose a metric ruler, a stopwatch or a string to complete the task.
a. Exp. how you could experimentally determine the spring constant.
b. The spring-object is now arranged so that the object but none of the spring is immersed in the unknown fluid. Describe any changes that are observed in the spring-object system and explain why they occur
c. Exp. how you could experimentally determine the density of the fluid.
d. Show explicitly, using equations how you willuse your measurements to calculate the fluid density.

Answer 1

a)

pretty straightforword, kx1=m1g where m1 is the mass of the irregular object and x1 is the distance the spring stretches from rest length under the weight of the mass. You know m1, g, and you can measure x1, hence you can find k.

b)

Now once you "dunk" mass m1 into the fluid the buoyant forces of the liquid in the beaker will push up on m1, hence the spring length will shorten.

c) We can peform a force analysis on the system, with the following equation

kx2 + m2g = m1g

(You have to be careful with the sign in front of kx2, it depends on whether the spring is in compression (-) or extension (+), make sure you know where and what the rest length of the spring is.)

The buoyant force is m2g where m2 is the mass of the liquid displaced by the irregular mass. m2 can be broken down further:

m2 = p2*V

where p2 is the density of the unknown liquid and V is the volume of the irregular mass. How do you find V? Well m1 = p1*V you are given m1 and p1 so you have find V.

We know k, m1, V, and g, and you can measure x2, hence you can solve for p2 and you get the density of the liquid.

Answer 2

Well, you can use Hooke's law. F=k*x and F=m*a. The mass of the beaker is m, gravity is a, and the spring constant is k. You'll need to use Archemide's principle to figure out the water submerssion thing. And you'll have to combine these to figure out the spring constant. Have fun with the algebra.

Answer 3

wow u r smart