Answer to Question #154571 in Physics for Japhet

Question

1. A conical flask with a base of diameter 7.0 cm is filled to a depth of 10cm with a liquid of density 840 kg/m3. Find the total force due to the liquid on the base in Newton’s.
2. A tube 1.98 m long is sealed at one end. It is lowered mouth downwards into water of density 1000 kg/m3 when atmospheric pressure is 100,000 N/m2. If the water rises 0.98m in the tubes and the temperature remains constant. Find the depth of the top of the tube below the surface of the water.
3. a. A weight of 50N is suspended from a beam by a string. What horizontal force must be applied to the weight to keep the string at an angle of 40degrees to the vertical? What is tension in the string?

3.b. The resultant of two forces makes angles 30degrees and 45 degrees with them, and has a magnitude of 25N. Find the magnitude of the two forces.

Answer 1

1)

$$F=\rho g A h=\rho g (0.25\pi d^2) h\\F=0.25\pi(840)(9.8)(0.07)^2(0.1)=3.2\ N$$

2)

$$P=\rho gh\\100000=(1000)(9.8)h\\h=10.2\ m$$

3) a)

$$F=50\tan{40}=42\ N\\T=50\cosec{40}=78\ N$$

b)

$$F_1\sin{30}=F_2\sin{45}\\\sqrt{2}F_2=F_1\\25=F_1\cos{30}+F_2\cos{45} \\25=\sqrt{2}F_2\cos{30}+F_2\cos{45}\\F_2=12.9\ N\\F_1=12.9\sqrt{2}=18.3\ N$$