Calculate the gravitational force between these three masses

  • Thread starter hraghav
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  • #1
hraghav
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Homework Statement
Three masses are located as follows:
Mass 1 with ๐‘š1=5.25ร—106kg is at ๐‘Ÿโƒ—1=29.9m๐‘–ฬ‚+17m๐‘—ฬ‚. Mass 2 with ๐‘š2=5.53ร—106kg is at ๐‘Ÿโƒ—2=40.4m๐‘–ฬ‚+17m๐‘—ฬ‚. Mass 3 with ๐‘š3=3.2ร—106kg is at ๐‘Ÿโƒ—3=40.4m๐‘–ฬ‚+35.4m๐‘—ฬ‚. What angle does the net force on ๐‘š3 make with the positive x-axis ๐‘–ฬ‚? with the y-axis ๐‘—ฬ‚?
Relevant Equations
I calculated the magnitude of the net force on ๐‘š3 due to ๐‘š1 and ๐‘š2 to be 5.790N.
Fnet on3 = 1.2365i + 5.657j
for the angle with positive x axis I did: component of fnetx = (magnitude of fnet)*costheta
1.23651 = 5.790*costheta
1.23651/5.790 = costheta
theta = 77.668 degrees

for the angle with positive y axis I did: component of fnety = (magnitude of fnet)*costheta
5.657 = 5.790*costheta
5.657/5.790 = costheta
theta = 12.30 degrees

But I am still getting both wrong. My magnitude of the net force is correct. Could someone please help me with this and let me know where am I making an error?
Thank you
 
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  • #2
hraghav said:
What angle does the net force on ๐‘š3 make with the positive x-axis ๐‘–ฬ‚?
Measured anticlockwise from the positive x axis.
 
  • #3
haruspex said:
Measured anticlockwise from the positive x axis.
Sorry I am just confused what would the equation look like then? would it be -component of fnetx = (magnitude of fnet)*costheta?
 
  • #4
The components that you calculated place the resultant in the first quadrant. They would be correct if the gravitational force were repulsive instead of attractive. Make a drawing to see what's going on.
 
  • #5
hraghav said:
Sorry I am just confused what would the equation look like then? would it be -component of fnetx = (magnitude of fnet)*costheta?
No. As @kuruman indicates, you have the wrong sign on "Fnet on 3".
When you have corrected that, you still need to be careful deducing angles from their trig functions because of quadrant ambiguities.
 

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