A cube with a side length of 35 mm is in equilibrium in water as in the figure. If the sinking part of the cube is h=27 mm; a) Buoyant force acting on the earring Fk = N b) Density of the substanc from which the cube is madepcube Su kg/m3 h c) If a hemisphere with a diameter of 15 mm is removed from the top of the cube, the new weight of the cube W new N

Q2)A filament 0.5m long and having a cross-sectional area of 1mm2 was stretched to breaking. If the breaking stress for the filament was found to be 109 Pa, calculate the mass which was hung on the filament to break it. Assuming the filament stretched linearly up to breaking, calculate the amount by which the filament stretched. (Young’s modulus for the material = 6 x 1010 Pa) If the assumption in (b) was justified, what might the material have been? State in one word.

In the figure shown below, the homogeneous bars AB and BC are identical, each having a mass of 1o0 kg. The coefficient of static friction between the bar at Cand the horizontal plane is 0.50. 1.50 m 3 m 30° 1.50 m 30° Determine the smallest value of P for which the system will be in static equilibrium, in N. Determine the largest value of P for which the system will be in static equilibrium, in N.

A tri-metallic bar is uniformly compressed by an axial force P = 40 kN applied through a rigid end plate (see figure). The bar consists of a circular steel core surrounded by a brass and copper tubes. The steel core has a diameter of 30 mm, the brass tube has outer diameter of 45 mm, and the copper tube has outer diameter of 60 mm. the corresponding moduli of elasticity are E, = 210 GPa, Es = 100 GPa, and E. = 120 GPa. P= 40 kN Copper tube Brass tube Steel core 30 mm 45 mm 60 mm Calculate the compressive stress in the steel core in MPa due to the force P. А. 25.1 Calculate the compressive stress in the brass tube in MPa. A. 7.9 Calculate the compressive stress in the copper tube in MPa. 1. В. 28.3 С. 22.4 D. 21.8 2. В. 8.2 С. 9.8 D. 10.4 3. А. 12.5 В. 14.2 С. 16.4 D. 17.8 1A 1B 10 O 1D 2A 2B 20 2D ЗА O 3B O 30 O 3D O O O O O O O O O O O O

Question 4: A machine of 540 kg is bolted at the middle of two parallel simply supported steel beams. The clear span of the beam is 2.4 m. The moment of inertia of the cross-section of each beam is I = 4.2×10¯6 mª. The Young's modulus of the steel is E 200 GPa. When the machine is operating, it will generate a vertical force P(t)=Posinot. When the machine runs at 300 rpm, Po= 1500 N. Neglect the weight of the beams and assume 2% viscous damping in the system. Determine the amplitude of steady-state deflection of the beams at their midpoint when the machine runs at 300 rpm. machine 1.2 m = 1.2 m Steel beams

1. Given that the value of P on the figure below is equal to 15 kN which is applied to the centroidal axis of each segment of the rod which is made up of aluminum, bronze and steel which are rigidly connected. Determine the stress in each material in the rod. Steel A=300 mm2 Bronze Aluminum A=400 mm2 A=600 mm2 2P ЗР 4P P 3m+ 5 m 4 m-

There is no force on a beam, but the beam is subjected to a very large temperature difference above and below. As shown in the figure below, try to calculate the vertical displacement of the midpoint of the beam, assuming that the temperature coefficient of the entire beam is a = 11.7×10^-6 °F. Tip: See Mechanics of Materials for Beam Deformation Geometry

A closed cylindrical tank, placed horizontally, 400 mm in internal diameter and 2.2 mm thick is subjected to an axial compressive force (along its longitudinal axis) and uniform internal pressure. The stresses acting on an element of side is shown in the figure.a. What is the magnitude of the internal pressure in MPa?b. What is the applied axial force in kN? (detailed solution please)

The rigidity modulus of a material whose E = 2 x 106 kg/cm2 and Poisson's ratio is 0.25 will be (a) 0.8 x 106 kg/cm2 (b) 0.6 x 106 kg/cm? (c) 0.5 x 106 kg/cm2 (d) 2 x 106 kg/cm?

Kindly solve and explain the solution