| Problem statement Solution video |
DISCUSSION THREAD
Ask your questions here. Or, answer questions of others here. Either way, you can learn.
DISCUSSION and HINTS
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw a single free body diagram (FBD) of the bar and the particle.
Step 2: Kinetics (Work/energy)
- Looking at your FBD above, which forces, if any, do work that is not a part of the potential energy of the system? If there are none, then energy is conserved.
- Write down the individual contributions to the kinetic energy from the bar and particle, and add together for the total kinetic energy of the system.
- Define your gravitational datum line. Write down the individual contributions to potential energy from the bar, particle and spring, and add together for the total potential energy.
Step 3: Kinematics
Use the following rigid body kinematics equation to relate the angular velocity of the bar to the velocity of the particle B at position 2:
vB= vG + ωAB x rB/G
Step 4: Solve
From your equations in Steps 2 and 3, solve for the angular velocity of the bar.
Does the spring start unstretched? Also, there are equations online to account for masses on the end of rods in terms of the mass moment of inertia. This contribution would essentially take the transnational term of kinetic energy (V_b) and put it into the mass moment of inertia equation, correct?
It says in the problem statement that when the bar is in the horizontal position (position 1), the spring is unstretched.
Do not complicate the problem by bringing in equations that might be found somewhere online. Simply rely on the fundamentals. For this problem, T = T_bar + T_B, where:
T_bar = 0.5*(M*L^2/12)*omega^2
T_B = 0.5*m*v_B^2
and in STEP 3: Kinematics, you have: v_B = 0.5*L*omega
Let me know if this is not clear.