1.) A uniform plank of weight 70.0 N is 2000 mm long. It rests on a support that is 700 mm from end F. A load of 50.0 N is placed at end E of the plank.
At what distance from F must a 180 N weight be placed in order to balance the plank?
2.) A jet of water of cross-sectional area of 3.0 cm2 is directed normally against a wall. If the speed of the jet of water is 30 m s-1, what is the average force exerted on the water, assuming (unrealistically) that the water is stopped by the wall ( Density of water = 1000 kg m-3.) [2]
3.) An ice cube of mass 40.0 g floats on the surface of a strong brine solution of volume 250.0 cm3 inside a measuring cylinder. Calculate the level of liquid in the measuring cylinder
(i) before and [2]
(ii) after the ice is melted. [2]
(Assume density of ice = 900 kg m-3, density of water = 1000 kg m-3 and density of brine = 1100 kg m-3)
Answer:
(i) Floating ice displaces 40 g of brine since upthrust equals weight of ice.
Volume displaced = mass/ density = 40.0/1.100 = 36.4 cm3 [1]
Level on the measuring cylinder = 286.4 cm3 [1]
(ii) 40.0 g of ice forms 40.0 g of water when all of it is melted.
Volume of 40.0 g of water = 40.0/1.000 = 40.0 cm3 [1]
Level on the measuring cylinder rises to 290.0 cm3 [1]
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