Student Generated Solutions

The following are solutions for textbook problems written by students in the course:

• Problem No. 2/216 - submitted by Derek
• Problem No. 3/7 - submitted by RyanA
• Problem No. 3/24 - submitted by RyanA
• Problem No. 3/50 - submitted by Derek
• Problem No. 3/54 - submitted by Imtiaz Ahmed
• Problem No. 3/56 - submitted by Imtiaz Ahmed
• Problem No. 5/59 - submitted by Steve-O
• Problem No. 5/66 - submitted by Leonard Pinto
• Problem No. 5/81 - submitted by Leonard Pinto
• Problem No. 6/118 - submittted by Bradle Harner
• Problem No. 6/129 - submitted by Anonymous
• Problem No. 6/148 - submitted by Anonymous
• Problem No. 8/1 - submitted by Robert Shingleton
• Problem No. 8/3 - submitted by Robert Shingleton
• Problem No. 8/14 - submitted by Robert Shingleton
• Problem No. 8/19 - submitted by Dale Szul
• Problem No. 8/26 - submitted by Madhi Alhasan
• Problem No. 8/32 - submitted by Warren
• Problem No. 8/45 - submitted by Madhi Alhasan
• Problem No. 8/50 - submitted by Warren
• Problem No. 8/65 - submitted by Warren
• Problem No. 8/66 - submitted by Warren
• Problem No. 8/74 - submitted by ayu_djaputra

[Disclaimer: I have not yet checked through the details for all these solutions. Let us know if you find any errors. CMK]

Problem 3/233

When trying to solve this problem, I get stuck on how to incorporate the cable/wheel. I can find the momentum of the masses; do I use angular accelerate to solve it? Anybody know what to do?

Homework Problem 3/241

Suggestions:
Draw an FBD of the ball. Find the moment about point O of the forces acting on the sphere. Note that this moment does not have a z-component. What does this mean? [The z-component of the angular momentum about point O is constant.] Use this to find the new angular velocity of the ball about the z-axis through O.

Let us know if you have questions on this.

Homework Problem 3/236

Suggestions:
The problem is naturally broken into two time periods: i) From time of release of plug to a time immediately before impact of plug with block (time 1 to time 2), and ii) from time immediately before impact of plug with block to time immediately after plug is wedged into block (time 2 to time 3).

• From time 1 to time 2: During this time, energy is conserved for the plug. Use this to find the speed of the plug right before impacting block.
• From time 2 to time 3: During this time period, energy is NOT conserved (energy is rarely conserved during impact). However, if you make a system of the sphere, block, plug and arm you will see that there are no non-impulsive forces creating a moment about hinge O. Hence, angular momentum of the system about O is conserved.
  

Let us know if you have any questions on this.

Homework Problem 3/269

Suggestions:
Draw FBD's of A alone, B alone and A+B together. From these FBD's:

1. From A alone, you know that momentum of A is conserved in the y-direction.
2. From B alone, you know that momentum of B is conserved in the y-direction.
3. From A+B together, you know that momentum of A+B is conserved in the x-direction.
   

These give you three equations. The fourth equation is the coefficient of restitution equation relating the differences in the x-components of velocity for A and B.

Let us know if you have any questions on this.

Homework Problem 3/253

Any questions?

Homework Problem 3/205

Any questions?

Homework Problem 3/189

Suggestions:
Draw an FBD of the system of A+B together. From this FBD you see that linear momentum is conserved for this system in the direction of motion. Use this to find the common speed of A and B once they stick together.

Let us know if you have questions on this.

Homework Problem 3/177

Suggestions:

1. FBD: Draw an FBD of A, B and link AB. Determine which, if any, nonconservative forces that do work on the system.
2. Work-energy equation: Since there are no nonconservative forces that do work, the WE equation becomes T1 + V1 = T2 + V2 where: T1 = 0 and T2 = (1/2)*m*vA^2 + (1/2)*m*vB^2. Write down the potential energy of the system based on your choice of datum position (recommended datum position: horizontal line passing through B).
3. Kinematics: Look back at your WE equation in 2. At what position will B have its maximum speed? (Hint:  The system has its maximum kinetic energy when its potential energy is a minimum -- when A is at its bottom-most position. What is the speed of A at this position? Use this in your work-energy equation.) 
4. Solve: Use the WE and kinematics equations to find vB.

NOTE:  As A falls through the vertical slot, the speed of B reaches a LOCAL maximum value at y = 2/3 of the initial height of A (this comes from differentiating the work energy equation with respect to time and setting d_vB/d_t = 0, as required for a maximum). This is the answer that is reported in the textbook. However, as A continues to fall, the speed of B reaches its absolute maximum when y = -L giving vB_max = 5.49 m/sec. Following the hint in 3. above will give you this absolute maximum. We will accept either answer.

Let us know if you have any questions on this.

Homework Problem 3/161

Suggestions:

1. FBD: Draw FBD of system made up of A, B and both massless links. Determine which, if any, non-conservative forces do work.
2. Work-energy equation: You will find from you FBD that there are no non-conservative forces that do work. Therefore, the work-energy equation becomes T1 + V1 = T2 + V2 where: T1 = 0 and T2 = (1/2)*mA*vA^2 + (1/2)*mB*vB^2. Write down the potential energy of the system at states 1 and 2. This will depend on your choice of datum position (I recommend a datum position that passes through point O.)
3. Kinematics: You need to determine the relationship between vA and vB at position 2. Hint: Look for the instant center of link BC to determine the velocity of point B at position 2.
4. Solve: Use the work-energy and kinematics equations to find vA.
   

Homework Problem No. 3/120

Questions?

Homework Problem No. 3/104

Questions??

3/91

What am I missing here?

I found the friction force at just before point B and at just before point C, but I am consistently getting the wrong answer for the force just after point B.

I am using acceleration-normal = v^2/p. Is there a trick to finding the velocity just after point B?

Alex

Homework Problem 3/86

This may be trivial, since this problem is not being submitted for grading, but in the video, there is no force from gravity acting on the block. Why not?

Homework Problem 3/91

Any questions?

Homework Problem 3/77

Any questions?

Note added by CMK in response to comments added by Fady and Brandon:

Fady asks a very good question: why does the block slip outward when there are not forces acting outward? 

Brandon added a good comment where he used a "centripetal force" argument. As Brandon describes, the centripetal force is not a true force but is rather a kinematic force constraint.

Click here to see a variation on Brandon's argument based on Newton's laws. Let me know if this helps to better understand this problem.

Again, very good question and comment.

Homework Problem 3/57

Is there any force from friction in this problem? If so, why not?

Homework Problem 3/9

Suggestion:
Consider the FBD shown above for the cart, person and three cut ends of the rope. Using Newton's second law on an axis along the incline will give you one equation for the acceleration of the cart/man.

Chapter 3 Homework Problems - Common Access Point for Videos