Finding the horizontal accerelation using forces

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To find the horizontal acceleration of a 5.00 kg block acted upon by two forces, F1 (30.5 N at an angle) and F2 (47.5 N), the forces must be resolved into their components. The horizontal component of F1 was calculated incorrectly; it should be positive since it opposes the direction of F2. The correct approach is to subtract the horizontal component of F1 from F2 to find the net force. This net force is then divided by the mass to determine the acceleration, which will be directed to the left due to the larger magnitude of F2. The calculations must ensure that the correct components and directions are used to arrive at the accurate acceleration value.
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Homework Statement


Interactive Solution 4.11 offers help in modeling this problem.

Two forces, vector F 1 and vector F 2, act on the 5.00 kg block shown in the drawing. The magnitudes of the forces are F1 = 30.5 N and F2 = 47.5 N. What is the horizontal acceleration (magnitude and direction) of the block?

link to picture (let me know if it works): http://www.webassign.net/CJ/04_11.gif

Homework Equations


SOHCAHTOA equations
Newton's 2nd law: F=ma

The Attempt at a Solution


Because F1 is at an angle, I broke it up into its y and x components:

sin(-65)*30.5 = -27.6 N
cos(-65)*30.5=-12.89 N

Since the question only asks for the accerelation in the x direction, I got the following equation:
(-47.5 N+-12.89N)=m*a=5*a

Then I solved for a and got 12.078 m/s^2 in the x direction. But the website of my homework is telling me this is wrong. help?
 
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jenador said:
Since the question only asks for the accerelation in the x direction, I got the following equation:
(-47.5 N+-12.89N)=m*a=5*a

Then I solved for a and got 12.078 N in the x direction. But the website of my homework is telling me this is wrong. help?

Except your drawing shows the direction of the force F1 to be positive x.

This means that the horizontal component of F1 is + and that opposes the direction of F2.

Apparently you have taken the sum where the difference would seem to be the correct approach.
 
i did that too but the computer is telling me that's the wrong answer as well. is it possible that 65 is the wrong angle to use ?
 
Your question is asking for acceleration. You are giving force as an answer.
 
The horizontal component of the force F1 and the force F2 are in opposite directions, therefore you have to substract 12.89 N from 47.5 N, and divide that net force by the mass to get the magnitude of the acceleration. The direction is obviosly to the left since F2's magnitude is larger than that of F1s horizontal component.

This is my first post, I hope I helped, great forum btw.
 
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