# I could use some help on this Calculus problem

• Aug 30th 2007, 04:13 PM
I could use some help on this Calculus problem
The problem reads: A constant force with vector representation F=10i+18j-6k moves an object along a straight line from the point (2,3,0) to the point (4,9,15). Find the work done if the distance is measured in meters and the magnitude of the force is measured in Newtons. From this I got the force by using sqrt(10^2+18^2+(-6)^2)=2*sqrt(115)*N Additionally I got the distance to be sqrt((4-2)^2+(9-3)^2+(15-0)^2)=sqrt(265)*m And because J=m*N I got the answer (2*sqrt(115)*N)*(sqrt(265)*m)=10*sqrt(1219) J However, the answer book gives is 38 J so could someone tell me what I'm doing wrong
• Aug 30th 2007, 08:55 PM
TKHunny
Is the force parallel to the movement of the point?
• Aug 31st 2007, 12:49 AM
CaptainBlack
Quote:

The problem reads: A constant force with vector representation F=10i+18j-6k moves an object along a straight line from the point (2,3,0) to the point (4,9,15). Find the work done if the distance is measured in meters and the magnitude of the force is measured in Newtons. From this I got the force by using sqrt(10^2+18^2+(-6)^2)=2*sqrt(115)*N Additionally I got the distance to be sqrt((4-2)^2+(9-3)^2+(15-0)^2)=sqrt(265)*m And because J=m*N I got the answer (2*sqrt(115)*N)*(sqrt(265)*m)=10*sqrt(1219) J However, the answer book gives is 38 J so could someone tell me what I'm doing wrong

Work:

$
\bold{W}=\int \bold{F}.\bold{dx}
$

In this case we have constant force and a straight line so this reduces to:

$
\bold{W}=\bold{F}.\bold{d}
$

where $\bold{d}=(4,9,15) - (2,3,0)$

RonL