Dynamics And Kinematics Problem

AI Thread Summary
The problem involves calculating the displacement of a block accelerating from rest under the influence of an applied force and friction. The calculations show that the net acceleration is approximately 0.93 m/s², leading to a displacement of about 7265.63 meters over 125 seconds. Concerns were raised about a friend's note suggesting a displacement of only 78 meters, which is deemed implausible given the calculated acceleration. The discussion emphasizes the importance of precision in calculations, particularly in rounding. Overall, the solution provided appears to be correct, alleviating doubts about the accuracy of the answer.
Plutonium88
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Homework Statement


Given: m = 17kg Vi = 0 Fa=42N θ=25 Mu=0.15 T=125s

Diagram: http://s14.postimage.org/euy3whikh/New_Bitmap_Image.png

Find: Δd

a block accellerates from rest for 125s find the displacement. Frictional forces act on the block.
A force applied is 25 degrees above the horizontal. Find the displacement

Homework Equations


Fnet=Ma
Δ=vit+a/2(t)^2

The Attempt at a Solution



Fnety=Fn + FaSin25 -Fg = 0

Fn= Fg - FaSin25

Fnetx=mAx=FaCos25 - Ffr

Ffr=Mu*Fn

Ffr= Mu*(Fg - FaSin25)

mAx = Facos25 - Mu*(Fg-FaSin25)

Ax= (Facos25 - Mu*(Fg-Fasin25))/m

Ax= 0.93 m/s^2 [--->]

Δd = vit + Ax/2(t)^2

Δd = + Ax/2(t)^2

answer: Δd = 7265.63 m

I'm not sure if this is correct or not, but my friend took a note in which it was the same question and he wrote down 78m.. I've done this question by myself to check everything but it bothers me the answer was wrong on the note he took, can some one infrom me if this is the correct way and if i have the correct answer to this problem please?

Did i not take something into account maybe..?
 
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The only fault I can find in your working is that you cut Ax off at two decimal places then used it to get an answer you quote to 6. (7232 m is closer.)
For the block to travel only 78 m in 125 secs the acceleration would have to be tiny. Even if you neglect the sin theta term it still gives 6000m.
 
haruspex said:
The only fault I can find in your working is that you cut Ax off at two decimal places then used it to get an answer you quote to 6. (7232 m is closer.)
For the block to travel only 78 m in 125 secs the acceleration would have to be tiny. Even if you neglect the sin theta term it still gives 6000m.

Thank you very much for checking this out for me i appreciate it very much. This settles my uneasiness about the question llol.
 
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