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Trigonometric identities
Solve and prove trigonometric identities
1.) Cot(theta)sin(theta)cos(theta)=1-sin²(theta)
2.) Sin²(theta)sec²(theta)-1
3.) Tan(theta)+cot(theta)= csc(theta)sec(theta)
4.) 1+cot(theta)= csc(theta)(cos(theta) + sin(theta))
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Determine the product of inertia for the area with respect to the x and y axes
1. The following results were obtained from a tensile test on a mind steel specimen of original diameter 20mm and guage length 40cm. At The limit of proportionality, the load was 8000kg and the extension 0.045mm. the specimen yielded at a load of 8200kg and the maximum load withstood was 1500kg. When the two parts were fitted together af being broken, the length between guage points was found to be 6cm and the diameter at the neck was 1.60cm. calculate
1. Young's modulus
2. Stress at The limit of proportionality
3. The yielded stress
4. The strain at the limit of proportionality
The ultimate tensile stress
5. Percentage elongation
6. Percentage contraction.
1. A metallic bar 250mm long is rectangular, 30mm x 75mm in section. If is subjected to a uniform stress of 210N/mm^2 along its length, find the changes in dimensions of the bar. E = 205KN/mm^2 and poison's ratio is 0.3
2. A rapper rod having end diameters 8cm and 2.5cm Long. Determine it's extension under a tensile load of 1200kg. E = 2*10^6kg/cm^2
A weight of 500kg is hanging from three wires of equal lengths. The middle wire is steel while the outer wire are copper. If the diameter of each of the wires is 3cm. Determine the load shared by each wire. Take young modulus of steel = 21*10^5kg/cm^2 and Young modulus of copper = 12.6*10^5kg/cm^2
A tie on a vertical pressing machine is 150cm long and 5cm square in cross section. Determine the stress and extension produced in the bar when it is subjected to an axial load of 150kN. Take E = 2.1*10^5N/mm^2
A tapered pipe is bent at 600 in the vertical plane. The diameters of inlet and outlet are 200cm and 400cm respectively. The center of the outlet is 180cm above the inlet. The pressure at outlet Page 2 of 2 is 500Kpa. If the flow rate of 0.04m3/s, calculate the resultant force and direction of action of the force
Define registers and list down different types of registers with examples
A tapered pipe is bent 600 in a vertical plane.The diameter of inlet and out let pipe are 200cm and 400cm respectively. The centre of the outlet is 180cm above the inlet.The pressure at outlet is 500Kpa.If the flow rate of 0.04m3/s.Calculate the resultant force and direction of action of the force
