Analyzing Collisions and Energy Transfer in AP Mechanics Problems

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In summary: Or is there any other principle I can use ??In summary, the first conversation discusses two experiments involving a 2kg block, 8kg block, and a 0.1kg ball of clay on a frictionless surface attached to an ideal spring. In the first experiment, the clay hits and sticks to the 2kg block while the 8kg block is held still, causing the spring to compress 0.4m. In the second experiment, the 8kg block is free to move and the clay hits another identical 2kg block. The question asks whether the maximum compression of the spring will be greater than, equal to, or less than 0.4m, and what principle can be used to calculate the
  • #1
nns91
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Homework Statement



1. A 2 kg block and 8kg block are both attached to an ideal spring (k= 200N/m) and both are initially at rest on a horizontal frictionless surface. In an initial experiment, a 0.1kg ball of clay is thrown at the 2 kg block. The clay is moving horizontally with speed v when it hits and sticks to the block. The 8kg block is held still by a removable stop. As a result, the spring compresses a maximum distance of 0.4m.

In a second experiment, an identical ball of clay is thrown at another identical 2kg blcok, bu this time the stop is removed so that the 8kg block is free to move.

d. State whether the maximum compression of the spring will be greater than, equal to , or less than 0.4m. Explain briefly.

e. State the principle(s) that can be used to calculate the velocity of the 8kg block at the instant that the spring regains it original length. Write the appropriate equations and show the numerical substitutions, but do not solve for the velocity

2. A 5kg ball initially rests at the edge of a 2m long, 1.2m high frictionless table. A hard plastic cube of mass 0.5kg slides across the table at a speed of 26 m/s and strikes the ball, causing the ball to leave in the direction in which the cube was moving.

b. Determine the horizontal velocity of the ball immediately after the collision.
c. Determine the cube's speed and direction of travel (if moving) immediately after the collision.
d. Determine the kinetic energy dissipated in the collision.
e. Determine the distance between two points of impact of the objects with the floor


Homework Equations



Conservation of energy, momentum

The Attempt at a Solution


1.I solved part a,b,c already.

In part d, I guess it will less than 0.4 but don't know how to explain that.

I also need some hints on part e too

2. I solved part a which was a graph question.

Part b,c since I don't know the type of collision ( I think it is elastic) so I can't use conservation of momentum. ANy hint ??

Part d: I guess I will calculate KE of the cube initially and KE of the cube after collision and their difference is the answer right ??

Part e: I don't understand the question, can anyone explain for me ??
 
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  • #2
D. well, no calculation. Here is what I think. Since the stop is remove, then the block can move. Well, then there will be kinetic energy. So rather than having all the energy transfer to potential energy of the spring, it gets diverted to both the kinetic energy of the block and the potential energy. So, by intuition, it must be smaller.

And you can ALWAYS use conservation of momentum. momentum is conserved in both elastic and inelastic collision (or any motion for that matter). Energy is also conserve, however, in inelastic collsion, energy becomes heat...so teachers just tell you that it's not conserve. After all, no one want to calculate the heat loss. ._.

So, if it's elastic --> use energy and momentum conservation
Inelastic --> momentum conservation should be suffice for the AP curriculum.Edit: If it said frictionless, pretty much it means elastic for AP curriculum.
b. Use momentum conservation.
C. well, same as above
D. well, they kinda told you it's inelastic. So use b and c (the velocity you calculated) and calculate the difference in energy. (the final E - inital E is the Energy "dissipated"..or in words that human can understand..become heat)
E. umm use kinematic?
 
  • #3
For b, it will be something like m(cube)*v(cube,i) = m(cube)v(cube,f) + m(ball)v(ball)

but I don't know the final velocity of the cube which is after collision, how can I use conservation of momentum ??

Can I use conservation of Energy by using: mgh=(1/2) mv^2 ?
 
  • #4
nns91 said:
For b, it will be something like m(cube)*v(cube,i) = m(cube)v(cube,f) + m(ball)v(ball)

but I don't know the final velocity of the cube which is after collision, how can I use conservation of momentum ??

Can I use conservation of Energy by using: mgh=(1/2) mv^2 ?

Part D ask you to solve for the energy lost. So that's a hint that energy isn't conserve. So prob don't want to use energy conservation (or else they won't have part d)

And I just realize that it said cube and ball. SO I guess you need to take into consideration of rotation energy? o_O?
 
  • #5
Pard D, they ask for lost of KINETIC ENERGY only not the whole ENERGY. So what is your suggestion for part b without knowing velocity of cube after collision ??
 
  • #6
For number 1, part e, is the principle that I can use conservation of energy ??

For number 2, part b, can I use mgh=1/2 mv^2 ?? If not, what other way can I use ??
 
  • #7
Anyone figure anything out yet ??
 
  • #8
so I have figured out some parts

which left me with part e, question 2 and part e of question 1.

Part e question 2 is a projectile motion problem. Any hint on that ?? I cannot think of any way right now. Can I use the formula for Range to calculate ?? something like R= (v^2*sin2[tex]\theta[/tex]) / g

Part e question 1, can I use conservation of momentum. If so, what will be the final momentum ?
 

1. What is the purpose of solving old AP Mech problems?

The purpose of solving old AP Mech problems is to practice and improve your understanding of the subject matter. These problems are similar to those that may appear on the actual AP Mech exam, so practicing them can help you prepare and potentially improve your score.

2. How do old AP Mech problems help in understanding concepts?

Solving old AP Mech problems can help in understanding concepts by allowing you to apply what you have learned in class to real-world problems. This can help solidify your understanding and identify any areas that may need further review.

3. Are old AP Mech problems still relevant?

While some of the specific content in old AP Mech problems may be outdated, the general concepts and problem-solving techniques are still relevant. It is still beneficial to practice these problems as they can help you prepare for the current AP Mech exam.

4. Is it necessary to solve all old AP Mech problems?

No, it is not necessary to solve all old AP Mech problems. It is more important to focus on understanding the concepts and problem-solving strategies rather than trying to solve every single problem. Pick a few from each topic to practice and make sure you understand them thoroughly.

5. How can I access old AP Mech problems?

There are several ways to access old AP Mech problems. You can find them in review books, online practice tests, or on the College Board website. Your teacher may also have access to previous AP Mech exams for you to practice with.

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