A g h F O Name ME 274 Exam No 2 April 2 2026 PROBLEM NO 1 20 points Given A particle P with mass m is moving about a point O in a smooth slot with the following equation cos 2 A force F applied through a pin at the slot At this instant 0 it is rotating with a constant angular velocity of in the Find For the position of 0 you are asked to find the A which acts as an ideal pulley a height h above direction clockwise normal force on P due to the side of the slot and determine if the particle is touching the inside or outside of the slot You are asked to follow the steps provided below Solution STEP A Draw the free body diagram FBD for particle P on the diagram to the right In your FBD indicate the unit vectors 1 3 1 5 and 67 if pointing out of the page indicate this Note that you must include all forces on h your FBD to receive full credit even if you do not use them to solve the problem STEP B Circle the method below that you will use to solve the problem A n a Newton b Work Energy c Linear Impulse Momentum d Angular Impulse Momentum 2 pts O n oouToFpI E STEP C Based on your FBD write out the kinetics equations that you will use Ef r N2 Flosy mar 4 pts P 5 pts F mg P s r N Vi cosy ME 274 Exam No 2 April 2 2026 PROBLEM NO 1 continued Name print Last First r 2 2 2 4 0 3 ar 41 b d b d w 5 pts 4 d cos 20 r o i o G b d cos 20 2 d sin 20 STEP D Write out the kinematics equations that you will use STEP E Solve for the normal force acting on P by the side of the slot Write your answer as a vector bed in terms of its polar coordinates Use b 2 m d 1 m h 2m m 1 kg F 2 N and 1 Mtbtd 2 2 pts bed Matart 2bd 2 2 3 Fcosg E 4 74 1 3 5 Nz 3 5 mar 3 b 2 32 d T FI STEP F On which surface of the slot is P in contact Nz a Inner Surface b Outer Surface 2pts 3 Name print SOLUTION ME 274 Exam No 2 April 2 2026 PROBLEM NO 2 20 points Given Particle P of mass m slides with a speed of along a smooth horizontal surface onto a First Last smooth curved surface on a stationary cart A having a mass of 2m Note that A is able to slide along a smooth horizontal surface Assume that P remains in contact with A after sliding onto A Find It is desired to know the velocities of A and P when P has reached a straight vertical section of the sliding surface on A at a height of h above the horizontal plane on which P was initially sliding Please follow the steps outlined below in arriving at your answers Solution PART A Using the figure included to the right draw a free body diagram FBD of A and P together PART B Based on your FBD in Part a respond to the following three TRUE FALSE questions No justification is required for your responses B 1 TRUE or FALSE Mechanical energy is conserved for the system of A and P together No non conservative forces do work on system of A P B 2 TRUE or FALSE Mechanical energy is conserved for the system of P alone A does work on P B 3 TRUE or FALSE Mechanical energy is conserved for the system of A alone P does work on A B 4 TRUE or FALSE Linear momentum in the x direction is conserved for the system of A and P together No force acting in x direction on FBD of A P B 5 TRUE or FALSE Linear momentum in the x direction is conserved for the system of P alone Force of A on P applies a non zero impulse in x B 6 TRUE or FALSE Linear momentum in the x direction is conserved for the system of A alone Force of P on A applies a non zero impulse in x ME 274 Exam No 2 April 2 2026 PROBLEM NO 2 continued Name print SOLUTION Last First PART C Determine the velocities of A and P Write your answers as vectors STEP 3 Kinematics Since P is on the vertical section at position 2 STEP 2 Work energy equation Since mechanical energy is conserved STEP 2 Linear momentum in x direction Since 0 0 2 0 2 Combining 1 and 3 2 Using 2 3 4 2 2 2 79 02 2 13 0 2 23 02 2 8 2 Using the magnitude of the velocity of P at position 2 along with 4 and 5 In summary STEP 4 Solve 1 2 3 4 5 ME 274 Exam No 2 April 2 2026 PROBLEM NO 3 Name print Last First Part 3A 10 points To illustrate the usefulness of the moving reference frame kinematic equation reference frame equation is to be used to describe the attached to the front wheel rotating with constant Consider the front part of a bicycle Let XYZ be a fixed coordinate system that is attached to the bicycle frame To this end provide expressions for the following four terms in this acceleration equation using components of the moving coordinate system xyz Note that you are NOT asked to write down the final answer for the acceleration of point P 2 A biker turns the handlebars with angular speed 0 and angular acceleration 1 Let 234 be a coordinate system angular speed 0 relative to 567 The above moving absolute acceleration of a point 8 located on the perimeter of the wheel at an angle of 9 with respect to the 2 axis using an observer attached to this front wheel 3A I 3A II 3A III 3A IV 6 First Last Name print ME 274 Exam No 2 April 2 2026 Part 3B A pendulum is made up of a particle P having a mass of m that is attached to a rigid link of length L and having negligible mass that is pinned to ground at O The pendulum is released from rest at an angle of measured from the vertical Neglect air resistance as P moves along its Draw a free body diagram of particle at release Show the path unit path Part 3 B 1 1 point vectors for P in your FBD a sin b cos c 0 d a sin b cos c 0 d Part 3 B 4 1 point The tension in the cord at release is At release a n 0 so the net force in the e None of the above normal direction must be zero Along the cord tension T balances the component of weight in that direction …