Unformatted text preview: ME 270 – Fall 2009
Examination No. 3
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PLEASE CIRCLE THE NAME OF YOUR INSTRUCTOR
Jones Li Murphy Krousgrill INSTRUCTIONS Nauman Begin each problem in the space provided on the examination sheets. If additional space is
required, use the yellow paper provided to you.
Work on one side of each sheet only, with only one problem on a sheet.
Each problem is worth 20 points.
Please remember that for you to obtain maximum credit for a problem, it must be clearly
presented, i.e.
•
•
•
• the coordinate system must be clearly identified.
where appropriate, free body diagrams must be drawn. These should be drawn
separately from the given figures.
units must be clearly stated as part of the answer.
you must carefully delineate vector and scalar quantities. If the solution does not follow a logical thought process, it will be assumed in error.
When handing in the test, please make sure that all sheets are in the correct sequential
order and make sure that your name is at the top of every page that you wish to have
graded. Problem 1 ________
Problem 2 ________
Problem 3 ________
Total ____________ ME 270 – Fall 2009
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Examination No. 3
Problem 1a
Kinematics (6 points). A pin travels along a path denoted by the expression , where r is in meters and θ is in radians. When θ = π/6 radians, rad/s and rad/s2, please determine the velocity vector in polar coordinates and the acceleration vector in polar coordinates. ME 270 – Fall 2009
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Problem 1b – Kinematics (4 points). A vehicle starts at rest on a horizontal circular track with a radius of 80
m. If the car increases its speed at a uniform rate to reach a speed of 80m/s in 10 seconds, determine the magnitude of the total acceleration when t =10 seconds. = ME 270 – Fall 2009
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Problem 1c – Kinetics (6 points). Please determine the magnitude of the acceleration of the 100
lb block for the two cases shown (3 points each case). a100 case (a) = a100 case (b) = ME 270 – Fall 2009
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Problem 1d – Kinetics (4 points). Determine the constant speed the block must have if there no normal force at point B. VB= ME 270 – Fall 2009
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3 and y = 2 + 2t2, 2. For the device shown, the motion of the pin P is governed by x = 0 + t
where x and y are measured in inches and t is in seconds. Please place your answers on the lines provided. y x . Please complete the following problems: 2a. The position in rectangular coordinates when t= 2 seconds (2 points). r = 2b. The velocity vector in rectangular coordinates when t= 2 seconds (2 points). ME 270 – Fall 2009
Examination No. 3
2c. The magnitude of the velocity Name
when t= 2 seconds (2 points). 2d. The acceleration vector in rectangular coordinates when t= 2 seconds (2 points). 2e. The magnitude of the acceleration when t= 2 seconds (2 points). 2f. The rate of change of the speed of P, , when t= 2 seconds (5 points). ME 270 – Fall 2009
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2g. The radius of curvature of the path ρ when t= 2 seconds (5 points) ME 270 – Fall 2009
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3. The block shown is sitting inside a cone section. At the moment of interest the block is a fixed distance (0.2 meters) from the axis of rotation and rotating at a constant angular velocity. The block has a mass of 2
kg. The outside angle of the cone is 30° as shown. Please show all work as you complete 3a and 3b. 3a. Consider the situation when there is no reliance on friction μk,s=0. Begin with a free
body diagram for the case with no friction (4 points). Determine the angular rate of rotation, ω, to keep the box at its current location when there is no frictional force (6 points). ME 270 – Fall 2009
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3b. Consider the situation when friction is required to keep the block in place (still rotating with constant angular velocity) and the friction coefficients (static and kinetic) are μk,s=0.5. Begin with a free
body diagram for the case where friction prevents the block from moving (4 points). Determine the maximum angular rotation that can be achieved without allowing the block to slip (6 points). ME 270 – Fall 2009
Examination No. 3
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This note was uploaded on 12/21/2011 for the course ME 270 taught by Professor Murphy during the Fall '08 term at Purdue.
 Fall '08
 MURPHY

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