For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. 8 kN 10 kN 8 kN to to to 24 kN m A E -3 m 3 m- 3 m-3 m-

A circular log floating in water is neutrally buoyant. Our ancestors found that by having half a log with semi-circular cross section and hollowing out the interior, it became stable so that they could use it to migrate across oceans. The reasons for it to become stable are: (i) (ii) (iii) (iv) It lowers the centre of gravity G so that it is below the centre of buoyancy B. It lowers the centre of gravity G so that it is below the metacentre M. It increases the metacentric radius BM. It enables the shifting of the centre of buoyancy B laterally to produce a restoring moment when it is tilted. (A) (B) (C) (D) (i) and (ii) (ii) and (iii) (iii) and (iv) (iv) and (i)

Drop-load (I)This exercise is part of a series of problems aimed at modelling a situation by progressively refining our model to consider more and more parameters. This progressive approach is very close to what professional scientists do! Context We want to lower a suspended load in a controlled way so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on a horizontal surface. Information The masses of the charges A and B are known.The pulley is a ring of mass mp and radius R that can rotate without friction.The surface on which mass A is placed is horizontal.There is no friction between mass A and the surface on which it is placed.The string attached to mass A is perfectly parallel to the surface on which the mass rests. SchematizationDraw a diagram of each object that interests us. Draw x- and y-axes for each object. Draw and name each force…

You are learning to play the violin. One end of the string is vibrating from the bow running along one end. The other end is tied down. The length of the string we will be looking at is 30 cm and the total mass of the string is 0,32 g. We will be modeling this as a standing wave on a string. You being to play the violin and play a note which has a frequency of 440 Hz. You (having incredible eyesight) see that there are 3 anti-nodes on the string forming a perfect sinusoidal wave (shown in diagram). L i) What is the wavelength of this standing wave? ii) What is the speed of the traveling waves that make up this standing wave? iii) What is the tension of the string? iv) Suppose you increase the tension of the string until you get a new standing wave. Will this standing wave have two antinodes or four antinodes? Explain. (You are still at a frequency of 440 Hz)