Problem statementSummary sheet for work/energy 1Solution video |

**DISCUSSION THREAD**

Any questions?? Please ask/answer questions regarding this homework problem through the "Leave a Comment" link above.

Problem statementSummary sheet for work/energy 1Solution video |

**DISCUSSION THREAD**

Any questions?? Please ask/answer questions regarding this homework problem through the "Leave a Comment" link above.

Problem statementSummary sheet for work/energy 1Solution video |

**DISCUSSION THREAD**

Problem statementSummary sheet for Newton's lawsSolution video |

**DISCUSSION THREAD**

**Discussion**

**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

* Step 3: Kinematics* - It is recommended that you use the

* 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.

Problem statementSummary sheet for Newton's lawsSolution video |

**DISCUSSION THREAD**

Any questions??

As P moves around on the circular track, two things occur:

- The normal force
*N*on P due to the circular guide is proportional to the centripetal acceleration of P:*N = mv*.^{2}/R - A friction force opposes its motion, where the sliding friction force is proportional to the normal force between the circular guide and P:
*f = μ*_{k}N = mμ_{k}v^{2}/R.

From this, we see that the friction force goes to zero as the speed goes to zero. What does this imply about P coming to rest? Can you see this in the animation of the motion below?

*HINTS*:

You will need to use the chain rule of differentiation to set up this problem: *dv/dt = (dv/ds)(ds/dt) = v (dv/ds)*.

Problem statementSummary sheet for Newton's Law - 2Solution video |

**DISCUSSION THREAD**

**Discussion**

**FOUR-STEP PLAN**

* Step 1: FBD* - Draw

* Step 2: Newton* - From each FBD, write down the Newton's equation for components along the incline. Recall that the pulley has negligible mass.

* Step 3: Kinematics* - You will need to use the cable-pulley system kinematics that we worked with earlier in the semester. Please review the material from Section 1.D of the lecture book to relate the accelerations of blocks A and B.

* Step 4: Solve *- Combine your equations from Steps 2 and 3 to solve for the accelerations of blocks A and B.

Problem statementSummary sheet for Newton's Laws - 2Solution video |

**DISCUSSION THREAD**

In the animation of the simulation shown below, the RED vectors shown are the forces of reaction *acting on particles A and B* (such as the force on each particle by member AB, and the normal forces of reaction by the floor and wall).

Problem statementSummary sheet for Newton's Laws - 1Solution video |

**DISCUSSION THREAD**

Since the motion of P is being described here in terms of polar variables of *r* and *θ*, it is recommended that you use a polar description for your forces and acceleration.

Use the Four-Step solution plan outlined in the lecture book:

* Step 1 - FBD*: Draw a free body diagram of C. NOTE: The arm rotates about a vertical axis, meaning that the arm moves in a horizontal plane; that is, the gravitational force acts perpendicular to the plane of the paper.

* Step 2 - Kinetics (Newton)*: Resolve the forces in your FBD into their polar components. Sum forces in the

* Step 3 - Kinematics*: Use the polar kinematics descriptions of

* Step 4 - Solve*. When solving for the normal force,

Problem statementSummary sheet for Newton's Laws - 1Solution video |

**DISCUSSION THREAD**

Problem statementSummary sheet for 3D MRF kinematics-2Solution video |

**DISCUSSION THREAD**

Any questions??

**Discussion and hints:**

Your first decision on this problem is to choose your observer. Since an observer on the plate will have the simplest view of the motion of the insect, attaching the observer to the plate is recommended. Also, attach your *xyz*-axes to the plate.

Next write down the angular velocity and angular acceleration of the plate. Based on what we have been doing up to this point in Chapter 3, hopefully it is clear that the plate (and observer) has two components of angular velocity: *Ω* about the fixed *X*-axis and *θ_dot* about the moving *z*-axis. Take a time derivative of the angular velocity vector to find the angular acceleration of the plate (observer).

Following that, determine the motion of the insect as seen by the observer on the plate.

Use these results with the moving reference frame kinematics equation to determine the velocity and acceleration of the insect.