Question

What is the velocity of a 500kg elevator that has 4000 joules of energy?

Answer 1

Ok you have calculate a heihgt from the ground and then use it to get the value of velocity.

Explanation:

Step 1: `E =mgh` and `h= E/(mg)`

So if you put your numbers in the formula : `h = 4000J/500*10`
you will get `h=4/5` meters

Step 2: use this , If the elevator moves from top to the ground in a constasnt acceleration you will have all energy (4000 J) transformed into acceleration to speed up its motion.

(All potential energy will be turned into movement energy). As explained in this formula;

`mgh=( mv^2)/2` , solve out (v) from the equation

`v= sqrt(2gh) =sqrt(2*10*4/5)= 4m/s`

Answer the velocity of the elevator is `4m/s`.

Answer 2

`4 \ "m/s"`

Explanation:

We use the formula for kinetic energy, which states that,

`"KE"=1/2mv^2`

• `m` is the mass of the object in kilograms

• `v` is the velocity of the object in meters per second

And so, we got:

`4000 \ "J"=1/2*500 \ "kg"*v^2`

`v^2=(4000 \ "J")/(250 \ "kg")`

`=16 \ "m"^2"/s"^2`

`:.v=sqrt(16 \ "m"^2"/s"^2)`

`=4 \ "m/s"` (since `v>0`)