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

[Shah 72]

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.

 

[Shah 72]

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.

 

[skeeter]

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?

 

[Shah 72]

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)

This is the exact info in the textbook. And iam getting a different ans from the ans given in the textbook.

 

[skeeter]

(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