Kinetic Energy

Question

If a car has 53 J of kinetic energy, what will its new kinetic energy be if you double its speed?

How will the kinetic energy of the car change if you speed of the car is reduced to 1/3 of its original value?

How will kinetic energy of the car change if you triple the mass of the car?

What will the new kinetic energy of the car be if you half the mass of the car and quadruple its speed at the same time?

 

Answer 1

If you write down the formula for kinetic energy (and understand what it means) you will be able to easily solve these problems  

 

KE = (1/2)mv²  

 

This formula says that the kinetic energy is equal to one half times the mass of an object times the square of its velocity.  So what happens to KE if you double m?  Well, the m in the formula will be replaced by 2m, but everything else will stay the same.  So the new KE will be double the old KE.  This is called a linear relationship - if m changes by a scale factor k, then KE will change by the exact same scale factor.  

 

Now consider what happens if you double v.  Instead of v² you will have (2v)² = 2²v² = 4v².  So the KE will go up by 2² = 4.  This is called a square relationship - if v changes by a scale factor k, then KE will change by k².  

 

Now you should be able to easily work out these problems.  If you can't figure them out in your head then just write down the expressions for KE before and after the changes and see how they are related.