kg/m 3 The hydraulic oil in a car lift has a density of 8.30 times 102 kg/m3. Th
ID: 2245485 • Letter: K
Question
kg/m3
The hydraulic oil in a car lift has a density of 8.30 times 102 kg/m3. The weight of the input piston is negligible. The radii of the input piston and output plunger are 7.20 times 10-3 m and0.125 m, respectively. What input force F is needed to support the 26,500-N combined weight of a car and the output plunger under the following conditions? The bottom surfaces of the piston and plunger are at the same level. The bottom surface of the output plunger is 1.20 m above that of the input piston. A duck is floating on a lake with 15% of its volume beneath the water. What is the average density of the duck?Explanation / Answer
areas of pistons are a=pi*r^2 and A=pi*R^2, where r=7.2E-3 m, R=0.125m;
the pressure in the oil is p=w/A as well as p=F/a, where w=27000 N, F is input force;
therefore F=w*a/A for the same level;
F=26500*(7.2E-3/0.125)^2 =87.92 N
b) now suppose they are still at the same level, yet you increase w by ?= ?*A*h*g, where h=1.2m, and A*h is excessive volume of oil;
thus F1= (w + ?*A*h*g)*a/A = F + ?*a*h*g = 87.92 + 830*pi*(0.0072)^2*1.2*9.81= 89.51N
2)
V is the volume of the duck and d is its density of duck,
Then its mass = Vd.
When it floats mass of 0.15 V of water = mass of the duck.
0. 15 V x density of water = Vd.
0.15 x density of water = d.
Density of duck = 0.15 times the density of water.
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