Help with clarifying steps for 1-Dimensional Collisions without known mass

In summary, the conversation is about a practice question involving a head-on collision between two vehicles, one with twice the mass of the other. The final velocity of the lighter car is given, and the question is asking for clarification on how to solve for the masses in the equation. The tip given is to cancel out the masses to solve for the unknown variable.
  • #1
princesspeach13
1
0

Homework Statement



I have a practice question in front of me, with the answer and the steps to reach it but I am having a tough go trying to figure out how to do the steps myself. Can someone please clarify the outlined area of the following question?

In a crash, test car A, was initially moving 20m/s, and Truck B, with twice the mass of car A, was traveling in the opposite direction, during a head on collision. The vehicles were stuck together after the collision, and the final velocity of the car was 6m/s in the opposite direction.

Homework Equations



Pi = Pf
m1v1 + m2v2 = (m1+m2)Vf

The Attempt at a Solution


m(20) + 2mV(truck initial) = (m + 2m)(-6)
20m + 2MVti = -18m
20m/s + 2Vti = -18m/s
V2 = 19m/s

Where my brain doesn't click is where the author has solved out the masses. If you have two sets of masses on the left side of the equation, and only one on the left, how can you just drop them all together?
Im sure this is probably some stupidly easy answer but when I go back to this type of question it doesn't solve out properly in my head.

Tips??
 
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  • #2
m's will cancel out
20m-2mvt=-18m
(20-2vt) m=-18m
 
Last edited:

Related to Help with clarifying steps for 1-Dimensional Collisions without known mass

1. What is a 1-dimensional collision without known mass?

A 1-dimensional collision without known mass is a type of collision between two objects where the masses of the objects are not known. This means that the masses of the objects cannot be used to calculate the outcome of the collision.

2. What are the steps for clarifying a 1-dimensional collision without known mass?

The steps for clarifying a 1-dimensional collision without known mass are as follows:

  • 1. Identify the initial and final velocities of the objects.
  • 2. Use the conservation of momentum equation (m1v1 + m2v2 = m1v1' + m2v2') to solve for the final velocities.
  • 3. Use the conservation of kinetic energy equation (1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2) to solve for the final velocities.
  • 4. Compare the final velocities obtained from the two equations. If they are not equal, then the masses of the objects cannot be determined.

3. How do you handle uncertainty in a 1-dimensional collision without known mass?

In a 1-dimensional collision without known mass, uncertainty can arise from not knowing the initial or final velocities of the objects. To handle this uncertainty, it is important to use the conservation of momentum and kinetic energy equations to solve for the final velocities. These equations are based on the principle that the total momentum and kinetic energy of a system remain constant, regardless of any uncertainties in individual values.

4. Can you determine the masses of the objects in a 1-dimensional collision without known mass?

No, it is not possible to determine the masses of the objects in a 1-dimensional collision without known mass. This is because the conservation of momentum and kinetic energy equations do not depend on the masses of the objects, so they cannot be used to solve for the masses.

5. What are some real-life examples of 1-dimensional collisions without known mass?

Some real-life examples of 1-dimensional collisions without known mass include collisions between subatomic particles, collisions between photons and particles, and collisions between gas molecules in a gas mixture where the individual masses of the molecules are not known.

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