Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin.Write an expression for the work done by the repulsive force on the object as it moves from an initial position of x1 to a final position of x2.  If the object starts at a position of x1 = 8.5 m apart, how much work, in joules, is required by an external force to bring it to a position of x2 = 2.5 m apart when a = 19 and b = 11?  If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?

Question
Asked Oct 26, 2019
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  Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin.

Write an expression for the work done by the repulsive force on the object as it moves from an initial position of x1 to a final position of x2

 

If the object starts at a position of x1 = 8.5 m apart, how much work, in joules, is required by an external force to bring it to a position of x2 = 2.5 m apart when a = 19 and b = 11? 

 

If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m? 

 

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Expert Answer

Step 1

Given:

Mass of the object, m = 4 kg

Repulsive force, F = a/x2 + b/x

Step 2

The formula of work done:

F dx
W work done
.F Applied force
.dx Small displacement
help_outline

Image Transcriptionclose

F dx W work done .F Applied force .dx Small displacement

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Step 3

Calculation for the expression of work done:  

 Pluggin...

b
.dc
W =
x
Integrating
-2+1
b(In x)
W — а
-21
X1
1
=-a
1
+b(Inx-Inx
х, х,
1
W 3 а
1
bln
х, х,,
(i)
help_outline

Image Transcriptionclose

b .dc W = x Integrating -2+1 b(In x) W — а -21 X1 1 =-a 1 +b(Inx-Inx х, х, 1 W 3 а 1 bln х, х,, (i)

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