How Does Momentum Compare to Kinetic Energy in Stopping a Vehicle?

[Jimmy87]

Please could someone explain the following situation. A truck weighs 4 tonnes and travels at 18m/s. A car on the same road, weighs 1.4 tonnes and is traveling at 35 m/s. The car has more kinetic energy but less momentum. My book says that momentum is how hard it is to stop something which is where my confusion comes in. To stop the car would require a force over a certain distance to bring it to rest and the work done would be equal to the KE. Since the car has more kinetic energy the force will need to be applied over a longer distance (or a greater force over the same distance) so surely the car is harder to stop? But it has less momentum so according to that definition it shouldn't?

 

[ShayanJ]

If you take a constant force, then you have F=\frac{\Delta p}{\Delta t}. Because the final momentum is zero, it turns into |F|=\frac{p}{\Delta t}. So if you want to stop two things in equal times, it needs a greater force to stop the one with larger momentum. But because the energy it takes is equal to object's initial kinetic energy, it takes more energy for the one having more kinetic energy.
Its not a good idea to say "momentum is how hard it is to stop something" because there should be an exact meaning to the "hardness of stopping something" which can only be conventional and is almost of no use.
In fact its not a good idea to give such definitions for physical quantities. They're only defined in relation with other quantities.

 

[Bandersnatch]

You've got two cars. You try to bring them to a stop using the same force. You find out that one takes longer to stop, but over a shorter distance. The other you can stop faster, but it travels farther.
There's an obvious difference between those cars. You call the property that makes a car go longer momentum, and the property that makes it go farther - kinetic energy.

Whichever you choose to call "harder to stop" is a matter of context, really.
One requires more force to stop it in a given time interval, but the other requires more force to stop it over a given distance.

 

[Jimmy87]

You've got two cars. You try to bring them to a stop using the same force. You find out that one takes longer to stop, but over a shorter distance. The other you can stop faster, but it travels farther.
There's an obvious difference between those cars. You call the property that makes a car go longer momentum, and the property that makes it go farther - kinetic energy.

Whichever you choose to call "harder to stop" is a matter of context, really.
One requires more force to stop it in a given time interval, but the other requires more force to stop it over a given distance.

Thanks guys, that makes sense. Could someone also clarify the difference between force and impulse. Force is dp/dt whereas impulse is dp/dt x t. My book deals with them on separate pages but makes a statement which makes them sound like the same. It says the f= dp/dt and says that this means that a force changes your momentum. Later on its states the equation for impulse and says that an impulse changes your momentum. Looking at the equation, is the force the rate of change of momentum i.e. How quickly it is changing whereas impulse is simply the total change in momentum?

 

[ShayanJ]

force the rate of change of momentum i.e. How quickly it is changing

impulse is simply the total change in momentum

That's it!