# Collision with a pinned and unpinned rod on a frictionless surface

• n00bot
In summary, the conversation discusses a problem involving a collision between a small object and a long thin rod on a frictionless surface. The object has an initial velocity and sticks to the rod, with different scenarios for when the rod is pinned or unpinned. The questions revolve around the conservation of linear and angular momentum, the determination of energy lost during the collision, and the location on the rod that would result in maximum energy loss. The solutions involve using formulas for coefficient of restitution, kinetic energy, and torque to determine the energy loss and the effects of the pin and frictionless surface.
n00bot
1. The Problem: (Collision with a thin rod -- pinned and unpinned)
A small object with mass n and an initial velocity of v sticks to a long thin rod of mass m and length l. The motion takes place on a horizontal frictionless surface. Answer the questions for the situation where
a) the rod is pinned at its center (but able to spin frictionlessly), the object rebounds, and the coefficient of restitution is r.
b) The rod is not pinned and the object sticks to the rod.

2. The Questions:
1. In each situation, is linear or angular momentum conserved? Explain.
2. Determine the energy lost in the collision.
3. Where should the small object collide with the rod to maximize the loss of energy in the collision? Explain.

3. The Attempt at a Solution :
1. a) The pin applies force on the rod, so linear momentum is not conserved within the rod-object system (the pin transfers some momentum to the surface). Angular momentum is conserved since the rod is free to rotate.
b) Both angular and linear momentum are conserved: the rod is free to rotate, and free to move. Rotation and translation.

2. a) Elastic collision, so KEinitial = KEfinal. I assume energy would be transferred to the rod from the object, but the system is constant. Maybe?

b) Since it is a completely inelastic collision, I know that KEinitial > KEfinal. My best guess to determine loss of energy would be to set up a conservation of energy equation, and have mobj-initialvobj-initial2 + 0 = (mobj + mrod)vfinal2. I'd then solve for vfinal, and plug Kinitial=mobj-initialvobj-initial2
Kfinal= (mobj + mrod)vfinal Is that correct?

3. a) if KEinitial = KEfinal, then no energy would be lost, and it wouldn't make a difference where the rod was hit. But... what about the pin? (How could that be right?!)

b)I assume the max loss of energy would occur with a collision at the center, because that would cause the bar to rotate the least (or, not at all). I can't really figure out where to go with this, though, since there's no friction (so, where would the energy go?) How do I go about figuring this out?

Thanks

hehe, I am new here, so i hope we all can work together.

well i think in

1. a)

linear and angular is not conserved.
reason: energy loss during collision (sound, heat, etc) and total initial energy is not equal to total final energy

1. b)

linear and angular in conserved, since is inelastic collision with no friction on surface

2. a) use the coeficient of restitution formula $$\textrm{C.O.R.} = \frac{|\vec{v_2} - \vec{v_1}|} {|\vec{u_2} - \vec{u_1}|}$$

substitute v1 and v2 in kinetic equation... the differences will get the energy loss.

2. b) there is no energy loss.

3. a) the edge of the rod, hmm, i think we can explain by relationship using formula of torque, force, and energy i guess

3. b) anywhere is the same, i think xP
anyway, please help me if i was wrong somewhere and I'm sorry if I'm wrong.. and i also sorry because i don't know whether i can leave my answer or not.. because i think only tutor can post answer here.. notify me if i did something wrong..
thanks

for your question and for providing the necessary information to solve the problem.

1. In each situation, is linear or angular momentum conserved? Explain.
a) In situation a), linear momentum is not conserved within the rod-object system due to the presence of the pin. The pin exerts a force on the rod, causing a change in the linear momentum of the system. However, angular momentum is conserved since the rod is free to rotate without any external torque acting on it.
b) In situation b), both linear and angular momentum are conserved since there are no external forces or torques acting on the system. The rod is free to move and rotate without any external interference.

2. Determine the energy lost in the collision.
a) In situation a), the collision is elastic, so the initial and final kinetic energies are equal. Therefore, no energy is lost in the collision.
b) In situation b), since it is a completely inelastic collision, some energy is lost due to the deformation of the objects. The amount of energy lost can be determined by subtracting the final kinetic energy (which is zero) from the initial kinetic energy.

3. Where should the small object collide with the rod to maximize the loss of energy in the collision? Explain.
In order to maximize the loss of energy in the collision, the small object should collide with the rod at a point that will cause the rod to rotate the most. This would result in a larger deformation of the objects and thus a greater loss of energy. This point would be at the end of the rod, furthest from the pin, as this would cause the rod to rotate the most. However, since there is no friction in the system, the energy lost would not be significant. If there was friction present, the energy lost would be converted into heat due to the sliding motion between the objects.

## 1. What is a pinned and unpinned rod?

A pinned rod is a rod that is fixed or attached to a surface at one end, while an unpinned rod is free to move without any attachments.

## 2. What is a frictionless surface?

A frictionless surface is a surface that has no resistance to motion, meaning there is no force acting against the movement of an object.

## 3. How does a collision occur between a pinned and unpinned rod on a frictionless surface?

A collision between a pinned and unpinned rod on a frictionless surface occurs when the two rods come into contact with each other and their motion is affected by the forces generated during the collision.

## 4. What are the factors that can affect the outcome of a collision between a pinned and unpinned rod on a frictionless surface?

The factors that can affect the outcome of a collision between a pinned and unpinned rod on a frictionless surface include the mass, velocity, and angle of the rods, as well as the elasticity of the materials and the angle of collision.

## 5. How can the outcome of a collision between a pinned and unpinned rod on a frictionless surface be predicted?

The outcome of a collision between a pinned and unpinned rod on a frictionless surface can be predicted by using known equations and principles of physics, such as conservation of momentum and energy, to calculate the resulting velocities and directions of motion of the rods after the collision.

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