| Problem statement Solution video https://youtu.be/AvXha8hg5tQ |
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 system made up of the drum, block A and the spring.
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? Does the force of friction at the no-slip contact point do work? If there are none, then energy is conserved.
- Write down the individual kinetic energy expressions for the drum and block A, and add together for the total KE of the system.
- Define your gravitational datum line. Write down the individual potential energy expressions for the drum block A and the spring, and add together for the total PE of the system.
Step 3: Kinematics
Relate the speed of A to the angular speed of the drum.
Step 4: Solve
From your equations in Steps 2 and 3, solve for the velocity of block A at position 2.
The diagram does not have a gravity arrow, but the system would not move without gravity. Should we assume that gravity points downwards?
Good question; I think this is a safe assumption.
Can we make the assumption that the cable is inextensible?
Yes. Otherwise we would give you then stiffness of the cable
Is delta of the spring equal to d ?
No it is not. You have to use a similar analysis as in 5.H. You can solve for the velocity of the center of gravity and at the point the cable is in contact with the drum. You can use the relationship of the velocities at this point to derive the stretch in the spring.
Can we use kg when applying the kinetic energy for the drum at the instant center instead of the center of mass?
Use k_G to find the mass moment of inertia about G:
I_G = M*k_G^2
Then use the P.A.T. to find I_C, where C is the instant center.
since it is asking for speed, should our answer be positive?
Speed is a scalar, meaning it doesn't have a direction, so a negative speed doesn't really exist. So yes, it should be positive
Is the movement of the spring considered to be the same as d, or do we have to use a different approach to calculate the extension of the spring?