# A particle moves in the xy plane as shown in the figure below and experiences a friction force with constant magnitude 7.38 N, always in the direction opposite the object's velocity.

Calculate the work that you must do to slide the object at constant speed against the friction force as the object moves along the following paths.

(a) the purple path O to  followed by a return purple path to O

(b) the purple path O to  followed by a return blue path to O

(c) the blue path O to  followed by a return blue path to O

(d) Each of your three answers should be nonzero. What is the significance of this observation?

asked Oct 14, 2011 in Physics

Since the object is moving at a constant speed, we assume there is no acceleration,  therefore

Total Force = mass*acceleration
Total Force =mass*0
Total Force = 0

Frictional force = 7.38 N

Total Force = Force - Frictional Force = 0
so
Force = Frictional Force
Force = 7.38 N

To find work we use the following formula:
Work = Force * distance

Part A:
Using the coordinates given, we realize that the distance from O to A is 5 m, since the object goes from O to A and then back to O, we multiply 5 by 2, and get 10 m for the total distance (net displacement)  traveled in part A.

distance = 10 m
Work = 7.38 N * 10m = 73.8 J

Part B.
First find the net displacement  (total distance traveled.)
The purple path from O to C is 10 m.  And the return blue path can be found using the pythageoreom theorem:

a^2+b^2=c^2

√(25m+25m) = c

c=7m
Therefore the net displacement is 5m + 5m + 7m = 17m

Plugging this into the work equation we get:

Work = 7.38 N* 17m = 125.46 J

Part C is also solved the same way.
Work =   7.38 N  * 14 m

Part D: We learn that the force of friction is a nonconservative force, because the values are nonzero.

answered May 22, 2012 by ~Expert~ (1,479 points)
selected May 22, 2012