What is the Magnitude of the Acceleration in This Newton's Laws Problem?

[ednof690]

Problem: Three forces in an xy plane act on 3.10 kg mass. 16.90 N directed at 46 deg, 7.20 N directed at 119 deg and 9.20 N directed at 218 deg . (all angles are measured from the positive x-axis, with positive angles in the counter-clockwise direction.) Calculate the magnitude of the acceleration.

F1=16.90 cos 46 x+ 16.90 sin 46 y
F2= 7.20 cos 119 x +7.20 sin 119 y
f3= 9.20 cos 218 x + 9.20 sin 218 y


I keep getting the answer .422 m/s^2, however i am told this is incorrect. I calculated the x and y components for the forces, then added them independently and then I divided each by the mass (after converting to Newtons) which should give me the acceleration. I then calculated the magnitude by using the pythag. theorem. is there a step i am missing or am i completely off?

 

[Doc Al]

F1=16.90 cos 46 x+ 16.90 sin 46 y
F2= 7.20 cos 119 x +7.20 sin 119 y
f3= 9.20 cos 218 x + 9.20 sin 218 y

This seems OK. What did you get for the total force?

I keep getting the answer .422 m/s^2, however i am told this is incorrect. I calculated the x and y components for the forces, then added them independently and then I divided each by the mass (after converting to Newtons) which should give me the acceleration.

What do you mean "after converting to Newtons"? The mass should be in kg, as given. Perhaps here is your error.

 

[ednof690]

I have no idea why i converted to Newtons, once i calculated it using the mass in kg , I got the correct acceleration. In what situation would i have to convert kg to Newtons?

 

[Doc Al]

Since kg is a unit of mass, not force, you can't "convert" one to the other. Sometimes you may be asked to find the weight of a given mass, but that's gotten by $w = mg$.