Chapter 4 Homework

Homework H4.C - Fa24

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Problem statement
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FOUR-STEP PLAN

Step 1: FBD - Draw a free body diagram of particle P. Note that the slot is smooth (no friction), and that the system moves in a horizontal plane (no influence of gravity).

Step 2: Newton - Recommended that you use a set of xy-coordinate axes attached to slotted arm. Resolve your forces into xy-components, and write down Newton's 2nd law for P in terms of its xy-components.

Step 3: Kinematics - It is recommended that you use the moving reference frame velocity and acceleration equations for point P, with the observer being attached to the slotted arm:
vP = vO + (vP/O)rel + ω x rP/O
 aP = aO + (aP/O)rel + α x rP/O + 2ω x (vP/O)rel + ω x (ω x rP/O)
Along with the rigid body velocity and acceleration equations for link AP, you will be able to solve these equations for the xy-components of the acceleration of P.

Step 4: Solve - Combine your equations from Steps 2 and 3 to solve for the normal force acting on P by the slot and the force on P by link AP.

10 thoughts on “Homework H4.C - Fa24”

  1. How do you find (v_P/O)_rel? I have everything I need for v except (v_P/O)_rel, for which I got (v_P/O)_rel = d_dot*i (with i being in the direction of the slotted rod). But d_dot is unknown.

    My first thought was to write another equation for v_P and use point A as the reference point, but that ends up introducing another unknown variable (theta_dot).

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      1. Wouldn't that give more unknowns though? I set the equation up as v_P = V_O + (v_P/O)_rel + omega x r_P/O and v_P = V_A + (v_P/A)_rel + theta_dot x r_P/A and simplified it to (v_P/O)_rel + omega x r_P/O = theta_dot x r_P/A. Doesn't that still leave two unknowns ((v_P/O)_rel and theta_dot)? Or is there a different way to solve for it?

        1. Using these equations does involve having two unknowns. However, you can solve for theta_dot by setting the j components from the two velocity equations equal to each other. Then you can solve for the d_dot by setting the i components equal to each other. I believe you will have to do a similar process for the acceleration as well.

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        2. I think you can do this because the values have components in different directions (I and j) and thus you actually get more equations here and the same number of unknowns.

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