How Do You Calculate Final Speed from Work Done on an Object?

[alexphysics]

Finding Final Speed Using Work

A person pushes with a horizonal 25N force over a distance of 1.2m on a 4.5kg crate, intially at rest on a frictionless surface. What is the final speed of the crate?

heres my data list..

F=25N
delta d=1.2m
m=4.5kg
v1=0
v2=?
theta=0 degrees

i used the W=fxdeltadxcos(theta) formula to find out the work done was 30J.. but once i have work i don't no what to find next to find the final speed..

 

[Rudipoo]

There are two ways of approach. One is using the constant acceleration equation

(v2)^2=(v1)^2+2as

where a is the acceleration of the crate and s is the displacement caused by the acceleration, i.e.

v1 = 0, a = F/m (Newton's Second Law) = 25/4.5 = 50/9, s = 1.2, so

v2 = sqrt (2.4*50/9) = sqrt (120/9 ) = sqrt (120)/3

The other is to find the work done by the force = F.d = 25*1.2 = 30J
and then say this is the additional kinetic energy given to the crate. Since the crate was at rest, we can say

0.5*m*(v2)^2 = 30
v2 = sqrt ( 60/4.5 ) = sqrt (120/9) = sqrt (120)/3

 

[rock.freak667]

What is the work done by the force converted into? (If it is moving what kind of energy does it have?)

 

[Rudipoo]

Energy by virtue of its motion is called kinetic energy, and kinetic energy is given by the formula K.E. = 0.5mv^2 where m is the mass of the body and v is the velocity.