Problem 2 (6 points) The mass me is supported by a cantilever beam, as shown in the figure, and oscillates vertically. The beam has a length L, cross-sectional area A, second moment of area I, and a modulus of elasticity E. (a) If the mass of the beam is negligible, find the natural frequency of oscillation. (b) If the rod has a mass me, find the equivalent mass of the system and the natural frequency of oscillation.

• 2-40 Water is being heated in a closed pan on top of a range while being stirred by a paddle wheel. During the process, 30 kJ of heat is transferred to the water, and 5 kj of heat is lost to the surrounding air. The paddle-wheel work amounts to 500 N:m. Determine the final energy of the system if its initial energy is 12.5 kJ.

The electric motor exerts a torque of 800 N-m on the steel shaft ABCD when it is rotating at a constant speed. Design specifications require that the diameter of the shaft be uniform from A to D and that the angle of twist between A and D not exceed 1.5°. Knowing that t max S 60 MPa and G=77.2 GPa,determine the minimum diameter shaft that can be used.

5.63 A 3.00-kg box that is several hundred meters above the surface of the earth is suspended from the end of a short vertical rope of negligible mass. A time-dependent upward force is applied to the upper end of the rope, and this results in a tension in the rope of T(t) = (36.0 N/s)t. The box is at rest at t = 0. The only forces on the box are the tension in the rope and gravity. (a) What is the velocity of the box at (i) t = 1.00 s and (ii) ? = 3.00 s? (b) What is the maximum distance that the box descends below its initial position? (c) At what value of i does the box return to its initial position?

2.34A crank-rocker four-bar linkage is shown in two different postures for which theta2 = 150° and 0,240°. Determine theta 3, and theta 4 for the open posture and e, and o for the crossed posture.

During operation the jack hammer strikes the concrete surface with a force which is indicated in the graph. To achieve this the 2.8-kg spike S is fired into the surface at90 m/s (Figure 1) Determine the speed of the spike just after rebounding

Question 2: A student of weight 667 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force Fy on the student from the seat is 556 N. (2) Does the student feel "light" or "heavy" there? (b) What is the magnitude of Fy at the lowest point? If the wheel's speed is doubled, what is the magnitude Fy at the (c) highest and (d) lowest point?

3/145 A bead with a mass of 0.25 kg is released from rest at A and slides down and around the fixed smooth wire. Determine the force N between the wire and the bead as it passes point B.

The spring has a stiffness k = 50 N/m and an unstretched length of 0.3 m. It is attached to the 3.4-kg smooth collar and the collar is released from rest at A (theta = 0°). The motion occurs in the horizontal plane Neglect the size of the collar.(Figure 1) \text { Determine the speed of the collar when } \theta=60^{\circ}

Question 4: A banked circular highway curve is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)

In the flyback converter shown in the figure below, Vs = 15 V, N1/N2 = 2, R = 50, Lm = 500 uH, C= 200 µF, and fs 40 kHz.The diode is ideal: I.e., zero voltage drop VD =0V. For the case when the output voltage Vo = 5 V, determine the largest value ofload resistance R allowed while operating in the continuous inductor current mode. (Using a load resistance greater than thisvalue will result in discontinuous inductor current operation.) [Select the one best answer from the choices given below.]