Totally Inelastic Collisions question

• CaptainOfSmug
In summary, a 2000-kg truck is rear-ended by a 1000-kg car going 28m/s and the two vehicles stick together. The final speed of the car-truck combination is 9.33m/s. The kinetic energy of the two-vehicle system before the collision is 392000J and after the collision, it is 43500J. This is a perfectly inelastic collision, as the colliding particles stick together and lose kinetic energy. The coefficient of restitution is not zero, as it involves relative velocities, but it is a small value due to some kinetic energy being lost in the bonding of the two bodies.
CaptainOfSmug

Homework Statement

A 2000-kg truck is sitting at rest (in neutral) when it is rear-ended by a 1000-kg car going 28m/s .After the collision, the two vehicles stick together.
#1What is the final speed of the car-truck combination?
#2What is the kinetic energy of the two-vehicle system before the collision?
#3What is the kinetic energy of the system after the collision?
#4Based on the results of the previous parts, what can you conclude about which type of collision this is?
#5Calculate the coefficient of restitution for this collision.

The Attempt at a Solution

Okay, so for the record I got all these answers correct (masteringphysics) if you've had to use this horrendous program :p

#1So for the final speed of the car-truck combination:
1000(28)+2000(0)=m12(V12xf
=9.33m/s
#2 The kinetic energy of the two vehicle system before the collision:
Kcar=0.5(mv2)
.5(1000)(28)^2
=392000J
#3 KE after the collision:
Ktruckandcar=.5(1000+2000)(9.33)2
#4 what type of collision is it?
I know the answer is totally inelastic but I cannot figure out why? By my books definition the final velocity of the truck and car must equal 0? Am I wrong here or can someone explain this for me?
#5 Since the answer to the previous question was totally inelastic I can assume e=0, but when I calculate it out this is not the case. I need an explanation on this to help my understanding of this! Thanks in advance!

Hi CoS. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

from Wikipedia:-
In a perfectly inelastic collision, i.e., a zero coefficient of restitution, the colliding particles stick together. In such a collision, kinetic energy is lost by bonding the two bodies together. This bonding energy usually results in a maximum kinetic energy loss of the system.

Last edited by a moderator:
Thank you for your reply, but I'm wondering when calculating the coefficient of restitution which is e=(V12xf)/(v12xi) isn't zero or am I missing something? Isn't the velocity of the two cars 9.33m/s? Shouldn't it actually be zero for e to =0?

coefficient of restitution involves relative velocities. When the bodies stick together their relative velocity is zero. After the collision they are often moving but locked together, so while some K.E. may be lost, it is not all lost.

Last edited:

In a totally inelastic collision, the two objects stick together after the collision and move with a common final velocity. In this case, the final speed of the car-truck combination is indeed 9.33 m/s, which is not equal to 0. This is because in a totally inelastic collision, some kinetic energy is lost due to the deformation of the objects involved. In this case, the kinetic energy of the system after the collision is less than the kinetic energy before the collision, which is consistent with a totally inelastic collision.

To calculate the coefficient of restitution for this collision, we can use the formula e = (V12xf-V12xi)/(V21xi-V12xi), where V12xf is the final velocity of the car-truck combination, V12xi is the initial velocity of the car, and V21xi is the initial velocity of the truck. Plugging in the values, we get e = (9.33-28)/(0-28) = 0.33. This means that the coefficient of restitution for this collision is 0.33, which is less than 1 and consistent with a totally inelastic collision.

What is a totally inelastic collision?

A totally inelastic collision is a type of collision in which two objects collide and stick together, resulting in a loss of kinetic energy. This means that the final velocity of the objects after the collision is the same and the objects move as one unit.

What is the difference between a totally inelastic collision and an elastic collision?

In an inelastic collision, there is a loss of kinetic energy, while in an elastic collision, the total kinetic energy remains the same. In an elastic collision, the objects involved bounce off each other, while in an inelastic collision, they stick together.

What is the equation for calculating the final velocity in a totally inelastic collision?

The equation for calculating the final velocity of objects in a totally inelastic collision is v = (m1v1 + m2v2) / (m1 + m2), where m1 and m2 are the masses of the objects and v1 and v2 are their initial velocities.

What are some real-world examples of totally inelastic collisions?

Some real-world examples of totally inelastic collisions include car crashes, where the cars stick together after colliding, and bullet impacts, where the bullet becomes embedded in the target.

What factors can affect the amount of kinetic energy lost in a totally inelastic collision?

The amount of kinetic energy lost in a totally inelastic collision can be affected by factors such as the mass and initial velocity of the objects, the angle of collision, and the materials of the objects involved.

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