Two forces, F1 and F2, act on the 5.00 kg block shown in the drawing. The magnitudes of the forces are F1 = 69.0 N and F2 = 24.5 N. What is the horizontal acceleration (magnitude and direction) of the block? F1 is pointing at the top left corner of the box forming a 65 degree angle with the parallel of the top of the box and the corner, F2 is pointing at the middle of the right side of the box.

2 questions: Do I subtract F1 (29.16) - F2 (24.5) Or do I subract F2 - F1? This would make a difference in a negative sign.

2) How do I determine then if the acceleration direction is right or left?

Physics Please Help - drwls, Saturday, January 21, 2012 at 12:51pm
Add the x components of F1 and F2. Then divide the result by the mass, 5 kg.

I would need to see the drawing to give you a more explicit answer. It does not matter what part of the block the vector arrow touches. It is the direction of the arrow that counts.

Physics Please Help - Nilan, Saturday, January 21, 2012 at 1:08pm
Force 1 is pushing on the top left corner of the box. The arrow forms a 65 degree angle with the verticle (as if the box were extended straight left, from 9:00 to the arrow = 65 degrees)
I found F1 horizontal component to be 69 cos 65 = 29.16 N

F2 is pushing to the left. F2 = 24.5 N

Am I right if I combine 29.16 - 24.5 (since it's pushing left) and divide by 5 to get 0.932 m/s^2 acceleration.

Then, since the F1 pushing right (29.16 horizontal component) is greater than the 24.5 pushing left, the direction is RIGHT. Is this correct?

To determine the horizontal acceleration of the block, you need to consider the individual components of the forces.

1) To determine the net force in the horizontal direction, you need to add the horizontal components of forces F1 and F2. Since F1 is at an angle with the horizontal, you'll need to find its horizontal component. To do this, multiply the magnitude of F1 by the cosine of the angle between F1 and the horizontal.

F1 horizontal component = F1 * cos(theta) = 69 N * cos(65 degrees) = 29.16 N

Now, subtract the horizontal component of F2 from the horizontal component of F1 to find the net force in the horizontal direction.

Net force = F1 horizontal component - F2 = 29.16 N - 24.5 N = 4.66 N

2) To determine the direction of acceleration (whether it is right or left), you need to consider the sign of the net force. If the net force is positive, the acceleration will be in the same direction as the net force (to the right). If the net force is negative, the acceleration will be in the opposite direction (to the left).

In this case, since the net force is positive (4.66 N), the acceleration will be in the direction of the net force, which is to the right.

Therefore, the horizontal acceleration of the block is 0.932 m/s^2 to the right.