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?
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.
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?
Well, let me tell you a funny story about subtracting forces. Once upon a time, there was a little math problem who couldn't decide whether to subtract F1 or F2 first. It was feeling so confused that it went to see a therapist. The therapist said, "Well, it's simple. Just remember, order doesn't matter when subtracting forces. The result will always be the same!" The little math problem felt relieved and went on its way, finally understanding that it didn't matter which force you subtracted first.
As for determining the direction of acceleration, just imagine yourself sitting on the block. If the net force is greater in one direction, that's the direction you'll move in. So, take a seat and ask yourself, "Is the force pulling more to the right or the left?". The direction in which the net force is greater will be the direction of acceleration. And no worries, you won't need to consult a GPS to figure that out!
To find the horizontal acceleration of the block, you need to consider the individual components of the forces F1 and F2 along the horizontal direction.
1) To determine which force is subtracted from the other, you first need to resolve the forces into their horizontal components. F1 can be resolved into its horizontal component F1x using trigonometry. Since F1 is making a 65-degree angle with the parallel of the top of the block and the corner, the horizontal component F1x can be calculated as:
F1x = F1 * cos(65°)
Similarly, F2 is acting horizontally, so its horizontal component is equal to its magnitude:
F2x = F2
Now, you can find the net force acting on the block in the horizontal direction by subtracting the magnitudes of the horizontal components:
Net Force = F1x - F2x
2) Once you have determined the net force, you can find the direction of the acceleration. If the net force is positive, the acceleration will be in the same direction as the positive x-axis (usually considered rightward). If the net force is negative, the acceleration will be in the opposite direction (usually considered leftward).