Work done by a general force

M

missrikku

Guest
Hello again! I just want to check if this is correct..

A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the pos direction of an x axis is applied to the block. The force is given by F(x) = (2.5 - x^2)i N, where x is in m and the initial position of the block is x = 0.

a) what is the kinetic energy of the block as it passes through x = 2.0 m?

b) what is the maximum kinetic energy of the block between x = 0 and x = 2.0 m


Wouldn't I get the same answer for both a and b?

I did the following:

** S = integral sign

W = S F(x)dx = Kf - Ki

with xi = 0 and xf = 2.0:

S F(x)dx = 2.5x -x^3/3 --> 2 1/3 J

Wouldn't the ans for both a and be be 2 1/3 J?

Thanks!
 

HallsofIvy

Science Advisor
41,626
821
Yes, since this is a horizontal surface, there is no change in potential energy so the change in kinetic energy must be the work done by the force. Integrating the force form the initial point to the last gives that work.

"Wouldn't the ans for both a and be be 2 1/3 J?"

Would it? Certainly the speed and energy will be increasing as long as the force is in the same direction but they will start decreasing when the force changes direction. Where does the force change direction?
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top