ME 230 - Dynamics
ME 230 - Dynamics Your Name:_________________
Tutorial 7 Section No.:_________________
Partners:_________________ _________________ _________________
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2-D Kinematics and Mass Moment of Inertia
1) At the instant shown, the length of the boom is being decreased at the constant rate of 6 in/sec and the boom is being lowered at the constant rate of 0.075 rad/sec. Knowing that ( = 30o, determine: a) the velocity of point B, and b) the acceleration of point B.
Choose and indicate appropriate reference frame(s).
Write the position vector [pic]for the boom tip in terms of symbols you define for the coordinate system you select.
Symbolically differentiate the position vector [pic] to determine the velocity vector [pic]for the boom tip.
Symbolically differentiate the velocity vector [pic]to determine the acceleration [pic]for the boom tip.
Numerically evaluate your equations to determine the velocity vector [pic] and the acceleration vector [pic]for the boom tip at the instant shown.
2) A cylindrical shell (pipe) and a solid cylinder, each of mass m and radius R, are released from rest on a surface inclined at angle ( and allowed to roll a distance of D feet. Determine the time (in seconds) it takes for each to roll this distance.
Write two general equations for the translational and rotational motion.
If there is no slipping, what equations exist that relate the angular displacement, velocity, and acceleration to the translational displacement, velocity, and acceleration.
Construct a free body diagram for the system.
Write the general equations for the angular acceleration of the pipe and cylinder in terms of the appropriate moments of inertia I and the other constants and variables.
Solve for the acceleration of the center of mass, a, for both the pipe and the cylinder by using appropriate equations for I.
From the above equations, and the experiment that you have set up, determine the time for each object to roll a proper distance down the incline.
Experimentally verify your results. Are your results dependent upon the mass of the rolling objects?
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