Question

A sign (mass 2400 kg ) hangs from the end of a vertical steel girder with a cross-sectional area of What is the stress within the girder? 0.011 m². Ignore the mass of the girder itself. The Express your answer to two significant figures and include the appropriate units. elastic modulus for steel is 2.0×10¹¹ N/m². If the girder is 6.40 m long, how much is it lengthened? Express your answer to two significant figures and include the appropriate units.

Answer 1

The stress within the girder is 2.14 × 10^6 N/m^2, and the elongation of the girder is approximately 0.0685 mm when a 2400 kg sign hangs from it.

Step-by-step explanation:

The stress within the girder caused by a hanging sign can be calculated using the equation for stress, which is stress = force / area. The force is due to the weight of the sign, which can be calculated by multiplying its mass by the acceleration due to gravity (9.8 m/s2). With a mass of 2400 kg, the force F is given by F = mass × gravity = 2400 kg × 9.8 m/s2 = 23520 N. The cross-sectional area of the girder is given as 0.011 m2.

The stress σ is therefore σ = F / A = 23520 N / 0.011 m2 which equals approximately 2.14 × 106 N/m2 (to two significant figures).

To determine the elongation of the girder, we use the equation ΔL = (F × L) / (A × Y), where ΔL is the elongation, L is the original length of the girder, A is the cross-sectional area, and Y is the Young's modulus for steel. The girder's original length is given as 6.40 m, and the Young's modulus for steel is 2.0× 1011 N/m2.

Thus, the elongation ΔL is ΔL = (23520 N × 6.40 m) / (0.011 m2 × 2.0× 1011 N/m2) which equals approximately 6.85 × 10-5 m or 0.0685 mm (to two significant figures).