Loughborough University
10MMB140 - Engineering Mechanics
Coursework weighting: Assignment 2 (Dynamics) 20%
The following coursework assignment must be handed-in to the General Office on the first floor of the Wolfson School of Mechanical & Manufacturing Engineering on Tuesday, 31 May. A green cover-sheet, available from the General Office, must be completed for each assignment and must be included in each assignment as the first sheet.
You should attempt all three questions. Two questions will be selected for marking
1. Work and Energy [50 marks]
In Fig.1, a 1300 kg car starts from rest at point 1 and moves without friction down the track. Determine (a) the force exerted by the track on the car at point 2, where the radius of curvature of the track is 6.4 m; (b) the minimum value of radius of curvature at point 3 to ensure that the car does not leave the track.
Figure 1
2. Vibration and Time Response [50 marks]
Figure 2 shows the elements of a displacement meter used to study the motion
yB = b×sinωt of the base. The motion of the mass relative to the frame is recorded on the rotating drum. If = 360 mm, = 480 mm, = 600 mm, m = 0.9 kg, c = 1.4 N×s/m and
ω = 10 rad/s, Determine the range of the spring constant k over which the magnitude of the recorded relative displacement is less than 1.5×b. It is assumed that the ratio ω/ωn must remain greater than unity.
Figure 2
3. Plane Kinetics of Rigid Bodies [50 marks]
In fig.3, the torsional spring has a stiffness k = 33 Nm/rad and is undeflected when the 6.4 kg uniform slender bar is in the upright position. If the bar is released from rest in the horizontal position shown, determine its angular velocity ω as it passes the vertical position. Assume friction to be negligible.
Figure 3