Which Truck Has Greater Momentum If Both Have the Same Kinetic Energy?

In summary, the larger truck has greater momentum due to its larger mass, as shown by the equation for momentum (P = MV) and the equation for kinetic energy (K.E. = 1/2 * mv^2).
  • #1
toittoiger
3
0
A simple question:

A small truck and a large truck have the same kinetic energies. Which truck has the greater momentum? Justify your answer.
 
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  • #2
Smells like homework...

Show us an attempt at solving the problem. Start with the equations you know for kinetic energy and momentum as functions of velocity, and relate them through that variable.
 
  • #3
toittoiger said:
A simple question:

A small truck and a large truck have the same kinetic energies. Which truck has the greater momentum? Justify your answer.
What is the expression for kinetic energies (ie in terms of ms, vs and ml and vl)? What is the expression for momenta of the two trucks? If the energies are equal, what is the ratio of the speeds vs/vl ?. Using that ratio, what is the ratio of their momenta?

AM
 
  • #4
I thought I saw another post just like this...
 
  • #5
Maybe I didn't. Anyway, set up your problem using the equation for kinetic energy.
Use m1 and m2... and to make things easy, let's say m2 = 1/2 m1.

[tex]K.E. = \frac{1}{2}mv^2[/tex]

Setting the two equation equal to each other...
[tex]\frac{1}{2}m_{1}^{2}v_{1}^2 = \frac{1}{2}*\frac{1}{2}m_{1}v_{2}^2[/tex]

The "m's" cancel and you get the velocities in terms of each other.
 
  • #6
yes there was a post exactly like this, i think he double posted it for one reason or another,

but i simply said that whenever a mass is increased the momentum is also increased - P=MV

of course i don't understand what they mean by larger truck, is it mass? or simply bigger?

because you can get equal KEs but haveing one of them going slightly faster, and the other with more mass, that when plugged into the momentum equation, the larger one will have more

offtopic said:
how do you do those javascript equations?
 
  • #7
You mean the math typesetting? That's Latex. This should get you started.
 
  • #8
toittoiger said:
A simple question:

A small truck and a large truck have the same kinetic energies. Which truck has the greater momentum? Justify your answer.

I assume you mean the larger truck has greater mass.

Let :

Larger truck : mass M, velocity V
Smaller truck : mass m, velocity v

Then,

[tex]\frac{1}{2}mv^2 = \frac{1}{2}MV^2[/tex]

[tex]V = v\sqrt{\frac{m}{M}}[/tex] -- eqn (1)

Momentum of the larger truck is MV, that of the smaller truck is mv.

Now, using eqn (1)

[tex]MV = Mv\sqrt{\frac{m}{M}} = v\sqrt{Mm} > v\sqrt{m^2} = mv[/tex]

Hence the larger truck has the greater momentum.

This doesn't apply in the trivial case when both trucks are at rest.
 

FAQ: Which Truck Has Greater Momentum If Both Have the Same Kinetic Energy?

What is the difference between kinetic energy and momentum?

Kinetic energy is the energy an object possesses due to its motion, while momentum is the measure of the object's mass and velocity. In other words, kinetic energy is the energy of motion, while momentum is the quantity of motion.

How are kinetic energy and momentum related?

Kinetic energy and momentum are related in that they both involve an object's motion. Kinetic energy is directly proportional to the square of an object's velocity, while momentum is directly proportional to the object's velocity. This means that as an object's velocity increases, both its kinetic energy and momentum will increase as well.

Can an object have kinetic energy without momentum?

Yes, an object can have kinetic energy without momentum. This can happen when an object is at rest, but has the potential to move. In this case, the object has kinetic energy but no momentum because momentum also takes into account the object's mass and velocity.

Which is more important in determining the behavior of moving objects: kinetic energy or momentum?

Both kinetic energy and momentum are important in determining the behavior of moving objects. Kinetic energy is important in understanding an object's potential to do work, while momentum is important in predicting how an object will move and interact with other objects.

How are kinetic energy and momentum used in real-life applications?

Kinetic energy and momentum are used in various real-life applications, such as in transportation systems, sports, and engineering. For example, the amount of kinetic energy and momentum a car possesses determines its speed and the force it exerts in a collision. In sports, understanding the relationship between kinetic energy and momentum can help athletes improve their performance. In engineering, both kinetic energy and momentum are important in designing and analyzing moving structures and machines.

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