Theory Based Kinetic Energy Question

[mike_302]

Homework Statement

Can a slow moving truck have more kinetic energy than a fast moving car? (assume lighter car, heavier truck)

Homework Equations

Ek=1/2mv^2

The Attempt at a Solution

Assume Ekcar < Ektruck

(1/2)m(car)v^2(car) > (1/2)m(truck)v^2(truck)

I don't know where to go from here to prove this though...

 

[NBAJam100]

Homework Statement

Can a slow moving truck have more kinetic energy than a fast moving car? (assume lighter car, heavier truck)

Homework Equations

Ek=1/2mv^2

The Attempt at a Solution

Assume Ekcar < Ektruck

(1/2)m(car)v^2(car) > (1/2)m(truck)v^2(truck)

I don't know where to go from here to prove this though...

Well, the answer lies within your equation of KE. KE=(.5)m*v^2... You were told that the truck is heavier than the car... So for the KE of the slower moving truck to be greater you would have to balance out its lower V by a higher (insert term) to get an equal or higher KE...

 

[LowlyPion]

Homework Statement

Can a slow moving truck have more kinetic energy than a fast moving car? (assume lighter car, heavier truck)

Homework Equations

Ek=1/2mv^2

The Attempt at a Solution

Assume Ekcar < Ektruck

(1/2)m(car)v^2(car) > (1/2)m(truck)v^2(truck)

I don't know where to go from here to prove this though...

Consider the magnitudes of |m_car| relative to the |m_truck| and the |V_car²| relative to the |V_truck²|

Isn't there a range of values of |m|/|m| > |v²|/|v²| that satisfies the condition of the predicate?

I'd say simply supply the range for which this is true.

 

[mike_302]

m(car)v^2(car) / v^2(truck) < m(truck)

That is what I have rearranged to... I see what NBA is getting at... if the truck was a million kilograms, the car 5 kg, and the speeds were like... 1 km/h and 2 km/h, then obviously it all works out. But is there anything more precise than that ?

OOPS, my inequality was the wrong way.

 

[NBAJam100]

m(car)v^2(car) - v^2(truck) < m(truck)

That is what I have rearranged to... I see what NBA is getting at... if the truck was a million kilograms, the car 5 kg, and the speeds were like... 1 km/h and 2 km/h, then obviously it all works out. But is there anything more precise than that ?

OOPS, my inequality was the wrong way.

Well sure there is a more precise answer out there but it doesn't seem to be looking for any sort of formal proof...

The questions states- "Can a slow moving truck have more kinetic energy than a fast moving car? (assume lighter car, heavier truck)"

So, can it? you tell me from what you have gathered above

 

[mike_302]

Yes. It can, if the mass was extremely large... lol, seems lacking to me, but I guess you are right.

 

[NBAJam100]

Yes. It can, if the mass was extremely large... lol, seems lacking to me, but I guess you are right.

Although I am not your instructor (or maybe I am... ) I would guess the point of this question is to illustrate that KE isn't based solely on velocity. Kinetic is relating to movement... so some might think kinetic energy is only based off of movement, but clearly from the equation KE is also dependent upon somethings mass (which might not be so intuitive).

So maybe its just to show that even though something is moving slower, it can actually have more kinetic energy. Then again I am not your teacher, just my take!

 

[mike_302]

That was scary! For half a minute I thought you might be my teacher! hahah, I figured that was the point it was trying to get across.

Thanks!

 

[NBAJam100]

That was scary! For half a minute I thought you might be my teacher! hahah, I figured that was the point it was trying to get across.

Thanks!

hahaha !

No Problem!