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.

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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 circle a followed by a return purple path to O

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

(c) the blue path O to circle c 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 by Mcats01 (62 points)
    

1 Answer

+3 votes
 
Best answer

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

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