determine the density of the liquid E Student Schedule Homework Help A. Ip http:

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determine the density of the liquid

E Student Schedule Homework Help A. Ip http://session.masteringphysics.com/myct/itemView? PHYS 213: Fluids a Mast gPh PHYS 213 (6 unread) File Edit View Favorites Tools Help Previous Next x Find plastic b Options Phys 213: Fluids and Thermal Physics, Fall 14 Close Homework 01: Fluids and Elas Item 8 previous 8 of 15 l next Item 8 Part B A plastic "boat" with a 25 cm square cross section floats in a d (cm liquid. One by one, you place 50-g masses inside the boat and measure how far the boat extends below the surface. Your data are as follows: d 0.0374 cm/g)n 0 cm Mass added, m (g) Depth, d (cm) 50 2.9 5.0 100 66 150 200 8.6 30 60 90 20 50 180 210 Graphing either m versus d or dversus m gives a straight line. In the graph shown above, we chose to plot d on the vertical axis and m on the horizontal axis. From the equation for the line of best fit given, determine the density pof the liquid Express your answer to three significant figures and include the appropriate units. Internet Explorer blocked a po from session.masteringphysics.com Allow once options for this site 3:43 PM 9/2/2014

Explanation / Answer

Given equation :
d = 0.0374m + 1.10

Slope of this d vs m plot = 0.0374

Here, 'd' is the depth(in cms) upto which the boat sinks into the water upon addition of mass 'm'(in grams)

When the boat sinks by depth 'd', the total volume of the boat which is under water = d*Area of cross section = 25d cm3

This is also the volume of the liquid being displaced by the boat.

So, mass of liquid displaced, m1 = volume of liquid displaced*density of liquid = 25d*row

So, bouyant force acting upwards = m1*g

Gravitational force acting downwards due to weight of boat = m*g

In equilibrium, these forces are equal. So,

m1*g = m*g

Thus, m1 = m

25d*row = m

So, row = m/(25d)

For any pair of values of 'm' and 'd' , the ratio m/d = 1/slope of d vs m plot

So, row = 1/(25*slope of d vs m plot) = 1/(25*0.0374) = 1.069 g/cm3

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