MHB Find Magnitude of Total Contact Force on 20kg Box in 3 Cases

AI Thread Summary
The discussion focuses on calculating the total contact force on a 20 kg box in three scenarios involving horizontal pulling and pushing forces. For case (a), the calculated contact force is 204N, while the textbook states it should be 196N. In case (b), the user arrives at 213N, but the textbook claims the answer is 183N, indicating a misunderstanding of the vertical component of the applied force. For case (c), the user finds 187N, while the textbook suggests 209N, again highlighting discrepancies in interpreting the forces involved. The conversation emphasizes the importance of understanding normal force calculations and suggests using free body diagrams for clarity.
Shah 72
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A box of mass 20 kg is at rest on a rough horizontal ground. Find the magnitude of the total contact force in each of the cases.
a) The box is pulled horizontally to the right by a force of 40N
b) the box is pushed to the left by a force of 50N at 15 degree above the horizontal .
c) the box is pushed to the left by a force of 50N at 15 degree below the horizontal.
 
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Shah 72 said:
A box of mass 20 kg is at rest on a rough horizontal ground. Find the magnitude of the total contact force in each of the cases.
a) The box is pulled horizontally to the right by a force of 40N
b) the box is pushed to the left by a force of 50N at 15 degree above the horizontal .
c) the box is pushed to the left by a force of 50N at 15 degree below the horizontal.
I have worked out the ans for a) will be 204N.
b) iam getting the ans 213N, but the textbook says 193N
c) I get the ans 187N , the textbook ans is 218N.
 
Shah 72 said:
A box of mass 20 kg is at rest on a rough horizontal ground. Find the magnitude of the total contact force in each of the cases.
a) The box is pulled horizontally to the right by a force of 40N
b) the box is pushed to the left by a force of 50N at 15 degree above the horizontal .
c) the box is pushed to the left by a force of 50N at 15 degree below the horizontal.
I have worked out the ans for a) will be 204N.
b) iam getting the ans 213N, but the textbook says 193N
c) I get the ans 187N , the textbook ans is 218N.

I don't get any of those values, yours or the text. I'm interpreting total contact force as the Normal Reaction Force the rough (assumedly horizontal) surface exerts upward on the box. Is that how your text defines it?

Is there more information that you haven't posted?
 
skeeter said:
I don't get any of those values, yours or the text. I'm interpreting total contact force as the Normal Reaction Force the rough (assumedly horizontal) surface exerts upward on the box. Is that how your text defines it?

Is there more information that you haven't posted?
The question is Q(3)
20210420_100046.jpg

This is the exact info in the textbook. And iam getting a different ans from the ans given in the textbook.
20210420_100046.jpg
20210420_100046.jpg
 
(a) normal contact force = weight = 20g = 196 N

(b) normal contact force = weight - vertical component of the applied force = 20g - 50sin(15) = 183 N

(c) normal contact force = weight + vertical component of the applied force = 20g + 50sin(15) = 209 N

may help your understanding if you sketched free body diagrams for each situation
 

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