Inelastic Collisions - Austin Community College District



Inelastic Collisions

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Equipment:

Computer running LoggerPro3: Two-Gate Timer Program Running in Gate Mode.

(2) Photogates linked to computer for data acquisition.

Dynamics Track with (2) Dynamics Cars, (1) Flag and (1) Gram Mass Set

Introduction:

When two objects collide they share a single interaction which creates equal sized forces directed in opposite directions. This interaction may speed-up one object and slow-down the other object, or, the interaction may slow-down both objects such as in a head-on collision of two cars. The force-time product of this interaction is known as “impulse” is defined as the size of the average force multiplied by the time-length of the interaction. The impulse size is equal to the size of the change in momentum. By Newton’s 3rd Law, each object receives equal sized but oppositely directed changes in momentum.

A. Pre-Lab Questions.

The following data was taken with two frictionless cars moving on a level surface. Car1, mass 4kg moves in +x direction with +3.0m/s velocity. Car1 collides with Car2, mass 2kg, which is initially at rest. Car1 and Car2 each move with a velocity of +2.0m/s after the collision.

A1-A3) Calculate the SI value of each cell in the table below. Show the calculation and the value in the cell.

Table1

|Object |Initial (before collision) |Final (after collision) |Final – Initial |

|p1 Car1 | | | |

| | | | |

| | | | |

|p2 Car2 | | | |

| | | | |

| | | | |

|Totals ( | | | |

| | | | |

| | | | |

A4) Explain why the overall momentum of both masses considered together was the same before and after the collision.

A5) Calculate the change in velocity of Car1 by filling in the blanks

Δv1 = v1f – v1i = ____________ – ______________ = __________________

A6) Calculate the change in velocity of Car2 by filling in the blanks

Δv2 = v2f – v2i = ____________ – ______________ = __________________

You should have found that the sizes of the changes in velocity were not equal. On the other hand, the momentum changes were equal in size but opposite in direction. The momentum concept was introduced due to this observation.

A7-A8) Calculate the kinetic energy of each car before and after the collision. Show calculation and SI answer in each cell.

Table 2. Write Energies in Joule Units

|Type |Initial (before collision) |Final (after collision) |

| | | |

|KE Car1 | | |

| | | |

| | | |

|KE Car2 | | |

| | | |

| | | |

|Thermal |0 |ΔUtherm = |

| | | |

|Column | | |

|Totals ( | | |

A9) Calculate the total energy before the collision and enter it into Table 2. Use energy conservation to calculate ΔUtherm. Show your calculation here.

A10) Was the increase in kinetic energy of Car2 equal in size to the decrease in KE of Car1? Why or why not?

A11) Was kinetic energy conserved in the collision? ____ Explain.

A12) Was energy conserved in the collision? ______ Explain.

B. Experiment: Complete Inelastic Collision.

Load Car1 with 800grams added mass. Car2 will be empty of extra mass and at rest before the collision. We will assume that the Car1 moves in the +x-direction.

Car1 mass m1 = _____________grams = ______________kg

Car2 mass m2 = _____________grams = ______________kg

v1i = ______________m/s v2i = 0m/s

v1f = v2f = ________________m/s

Calculate the following, showing calculation and units:

B1) Δp1 = m1(v1f – v1i) = (________)(_______– _________) = __________kgm/s

B2) Δp2 = m2(v2f – v2i) = (________)(_______– _________) = __________kgm/s

B3) Is it true that Δp1 and Δp2 are nearly equal in size but opposite in sign?_____

B4) What is the direction of the collision force on Car1 with respect to its initial (+x) velocity ? Is the collision force parallel or anti-parallel (opposite) to v1i?

B5) Does the collision force speed-up or slow-down Car1?

B6) Assuming the collision lasts 0.0055 seconds, calculate the size of the average collision force that acts on Car1 using Favg = Δp1/Δt. Show formula, calculation, and units.

B7) Assuming the collision lasts 0.0055s calculate the size of the average collision force that acts on Car2 using Favg = Δp2/Δt. Show formula, calculation, and units. What direction does this force act on Car2?

B8) If the collision-time were 10 times greater, all other things remaining the same, how would this affect the values of the collision force calculated in the last two questions?

C. Momentum and Velocity

Transfer your data from the previous page to the spaces below.

Car1 mass m1 = _____________grams = ______________kg

Car2 mass m2 = _____________grams = ______________kg

v1i = ______________m/s v2i = 0m/s

v1f = v2f = ________________m/s

Make the following calculations of the system-momentum P:

C1) Pi = m1v1i + m2v2i = (______)(_______) + (______)(_______) =___________kg·m/s

C2) Pf = m1v1f + m2v2f = (______)(_______) + (______)(_______) =___________kg·m/s

C3) Estimate the percent change in system momentum: ______. Was this an increase or a decrease in system momentum?___________What experimental factors might have caused this change?

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C4) Calculate the following energies:

Ki = ½m1(v1i)2 + ½m2(v2i)2 = ½(______)(______)2 + ½(______)(_______)2 =___________J

Kf = ½m1(v1f)2 + ½m2(v2f)2 = ½(______)(______)2 + ½(______)(_______)2 =___________J

C5) Estimate the percent change in system kinetic energy: ______. Was this an increase or a decrease in system kinetic energy? ___________ Where did this energy go to or come from?

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C6) How much thermal energy was created in the collision? ________________. Where did this energy come from?

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