Chapter 5 Homework

Homework H5.K - Sp 25

22 Comments
Problem statement
Solution video

DISCUSSION THREAD

Ask your questions here. Or, answer questions of others here. Either way, you can learn.

DISCUSSION and HINTS

The animation below shows the motion of the disk as it moves along the incline. Included in the video are the friction and normal forces (FF and FN) acting on the disk as it moves.

Recall the following four-step plan outline in the lecture book and discussed in lecture:

Step 1: FBDs
Draw a free body diagram (FBD) of the disk. In drawing your FBD, please note that the friction force is NOT proportional to the normal force N; that is, f ≠ μN. Why is that?

It is recommended that you choose a set of coordinates that are aligned with the ramp. For example, choose the x-direction down the incline and the y-direction   perpendicular to the ramp pointing up and to the right.

Step 2: Kinetics (Newton/Euler)

  • Based on your FBD above, write down the impulse/momentum equation in the x-direction for the disk.
  • Based on your FBD above, write down the angular impulse/momentum equation for the disk.
  • Combine the two equations above by eliminating the impulse of the friction force from the equations.

The above gives you a single equation in terms of two variables: vO and ωdisk.

Step 3: Kinematics
Note that the no-slip contact point of the disk with the incline is the instant center (IC) of the disk. Let's call that point C. Since C is the IC of the disk, you can readily relate the angular velocity of the disk to the velocity vector of the disk center O through:

vO= vC + ωdisk x rO/C = ωdisk x rO/C

Be careful with signs.

Step 4: Solve
From your equations in Steps 2 and 3, solve for the velocity of point O on the wheel at time 2.

22 thoughts on “Homework H5.K - Sp 25”

    1. You can use the kinematic equation posted below the problem or the concept of instantaneous centers to relate the velocity of the center of the disk to the angular velocity of the disk for BOTH the initial and final (after 12 seconds) states.

    2. You can use the kinematic equation posted below the problem or the concept of instantaneous centers to relate the velocity of the center of the disk to the angular velocity of the disk for BOTH the initial and final (after 12 seconds) states.

    3. I interpreted wdisk as the final angular velocity because they don't explicitly state the initial angular velocity.

  2. Can we put the final velocity in terms of the i and j vectors we defined to solve the problem?

    1. I'd say as long as you've clearly defined them in your system diagram or FBD, I don't see why not.

    2. I believe so, in step one it mentions that its recommended to choose your x-axis as down along the ramp and y-axis perpendicular and up to the right. If you look at the animation of the disk, the velocity of the disk moves in this defined axis.

  3. Based on the motion of the disk in the video, we can assume gravity to be present, correct?

    1. Yes, there must be gravity present for the disk to move down the ramp because there are no other forces acting in that direction.

    2. For problems like this where there is no slip, there must be friction, which would be caused by a normal force. Normal force wouldn't be present without gravity in this situation. If you are unsure or if gravity is not clearly noted, because sometimes it isn't, keep what I said above in mind.

      1

  4. Could we also approach this problem with work/energy? State 1 could be the disk initially rolling up, state 2 would be when it stops at the top. and state 3 would be the rolling disk at delta_t

    1. Keep in mind that the W/E equation relates change in speed for a change in POSITION. This problem needs a change the velocity for a change in TIME.

      1

    1. f = mu_s*N is the maximum possible friction (impending slipping). There is nothing in the problem that suggests impending slipping for the disk. Therefore, friction is simply an unknown reaction force and is known only to be LESS THAN mu_k*N.

      1

  6. Why is the frictional force always up the incline as the disk is rolling both up and down the incline in the animation?

    2. Wouldn't it be because the disk’s rotation would otherwise cause its point of contact to slip down the plane, friction acts up the incline in both the uphill and downhill cases to prevent slipping and supply the necessary torque for rolling without slip.

  7. The component of weight in the direction of the surface of the incline doesn't cause a moment, right?

    1. Depends on your choice of reference point.

      * If you choose the center of the disk, O, as the reference point, then weight does NOT create a moment. It just makes a component of force along the incline.

      * If you choose the no-slip contact point as the reference point, then, yes, weight DOES create a moment.

  8. do we include the initial velocity in our impulse momentum equation in the x direction?

    1. Absolutely. The impulse/momentum equation is related to the CHANGE in momentum. You need to include both the initial and final velocities in the equation.

  9. Would the friction applied in this problem remain constant due to the no-slip condition?

Comments are closed.