How much work is required to stop a moving block?

AI Thread Summary
To stop a 3kg block moving at 4 m/s, the work done must equal the change in kinetic energy, calculated as 24 Joules. The initial kinetic energy is determined using the formula 0.5 x mass x (final velocity squared - initial velocity squared). A constant friction force of 2 Newtons acting on the block allows for the calculation of acceleration using F=ma, resulting in an acceleration of approximately 0.67 m/s². The approach to solving both parts of the problem is confirmed as correct. Understanding the relationship between work, energy, and forces is crucial in these calculations.
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Homework Statement



a 3kg block moves initially at 4 m/s at t=0 and slides on a horizontal surface... Find the magnitude of word that must be done on the block to bring it to rest

Homework Equations


I believe we must use the equation w=Fs


The Attempt at a Solution



I drew the free body diagram and figured that the we have to find the opposing force and the relative displacement. I am having a hard time getting started with this problem. i know that [F]=[N][m] and =[m]
 
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Work done is equal to the change in kinetic energy.
What is the initial KE?
What is the final KE?
 
okay so i figured that the change in KE=.5 x m x (vf^2-vi^2)
for this problem it would equal 24J
 
Yes. It is correct.
 
There is an extention to the problem:

A constant friction force of 2 Newtons is exerted on the block by the surface find the magnitude of acceleration of the block

So I used F=ma where the force i used was 2 and the mass was 3 so id id

2/3 to find the acceleration which is .66666 is this the right method to answering this question?
 
nm i got the right answer thankyou!
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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