Head On Collision: Cars vs Trucks

[harsh95]

A large truck and a car,both moving with a velocity of magnitude "V",have a head on collision and both of them come to halt after that.If the collision lasts for 1s:
(a)Which vehicle experiences the greater force of impact?
(b)Which vehicle experiences the greater change in momentum?
(c)Which vehicle experiences greater acceleration?
(d)Why is the car likely to suffer more damage than the truck?
Please help me solve this with equations and statement.I a having trouble with Newton's third law!



I think Newton's third and second law are applicable here!

The Attempt at a Solution

 

[gneill]

We're waiting for your attempt at a solution... What are your thoughts on item (a)?

 

[harsh95]

For (a) Due to 3rd law of motion I think both will experience same force of impact! Every action has equal and opp. reaction.
For (b) Because truck's mass is more and velocity being same,so I think it will experience greater change in momentum.But I am unable to proof this with equation!
For (c)Not getting the question
For (d)Practically car would experience greater damage but I don't know why because acc to 3rd law they both should exert equal force

 

[gneill]

Your answer (a) looks okay.

For (b), I don't see any evidence in the question that the truck masses more than the car! The question says 'A large truck and a car...", but then it states that both are moving with the same velocity magnitude V, and that they come to a halt after colliding. That sounds like they have equal momenta, and if |V| is the same, then so is M.

 

[harsh95]

Sir,if it is given that mass of truck is greater then would it have a greater momenta? Also the collision lasts for 1 second,so how they have equal momenta?
Could please tell me the answer for (c) and (d)
I am preparing for Science Olympiad and "Law of motion" is one of the chapter in syllabus.
Am really confused between 2nd and 3rd law!

Because 3rd law states that every action has equal and opposite reaction then but then F=ma.Then if the Mass of object and the acceleration is greater then the object it is having head on collision with then how will they exert equal force?
I think if understood this concept I would be able solve this type of question! Please help
Thank you

 

[gneill]

Sir,if it is given that mass of truck is greater then would it have a greater momenta?

What is the formula for momentum?

Also the collision lasts for 1 second,so how they have equal momenta?

What are their momenta after the collision and they are both at rest?

Could please tell me the answer for (c) and (d)
I am preparing for Science Olympiad and "Law of motion" is one of the chapter in syllabus.
Am really confused between 2nd and 3rd law!

How you answer (c) and (d) depends upon your understanding of the question. If you think that the truck has a different mass than the car, then they would have to have different velocities in order for the magnitudes of their momenta to be equal. With different momenta you would expect there to be some "leftover" momentum after the collision, and the pair would continue to roll or slide along the road until friction brought them to a halt.

Because 3rd law states that every action has equal and opposite reaction then but then F=ma.Then if the Mass of object and the acceleration is greater then the object it is having head on collision with then how will they exert equal force?
I think if understood this concept I would be able solve this type of question! Please help
Thank you

Suppose you have one mass M that is ten times another mass m. If mass M is traveling at speed V, what speed would m have to travel in order to have the same magnitude of momentum?

If both M and m are brought to rest by colliding head-on, what is the change in velocity of each? Which had to accelerate (decelerate) more during the collision?

The third law concerns bodies that mutually interact; One body touches another and they apply equal and oppositely directed forces on each other. The second law concerns an unbalanced external force being applied to a body, without reference to what the "agent" is that's applying the force.

In reality, all real forces have "agents" of some form if you look hard enough. But it is often convenient to ignore the agent and consider just the disembodied force. An example is the force of gravity, where we simply place a force vector on the free body diagram and label it "mg"; we (usually) don't bother considering the third-law implications of the response of the Earth to the equal and opposite force being applied to it.

 

[harsh95]

Formula for momentum p=mv
If they are at rest then their momenta will be 0 because velocity is 0

"Suppose you have one mass M that is ten times another mass m. If mass M is traveling at speed V, what speed would m have to travel in order to have the same magnitude of momentum?"

Then it has to travel at velocity 10 times than the object of mass M for them to have same magnitude of momentum.

"If both M and m are brought to rest by colliding head-on, what is the change in velocity of each? Which had to accelerate (decelerate) more during the collision?"

The object with smaller mass had to decelerate more that is the object with mass "m" traveling at velocity "10v"

 

[Delphi51]

Curious question - "large truck" strongly suggests a much larger mass than a car, but according to conservation of momentum they would not come to a stop unless the masses were equal. Or are we to assume the car is severely damaged so friction becomes large and causes them to stop? I suspect an error has been made in writing the question.