In Figure 5.2a (reproduced below), two forces are applied to a box. In which direction will the box accelerate?

Question

BlackTom AI · Accepted Answer

In this setup, two forces are acting on the box via ropes attached at different points. The motion of the box is governed by Newton's second law: the acceleration is in the direction of the resultant (net) force, which is the vector sum of all applied forces.

Option 1: 'The box does not accelerate' would only be true if the net force were zero. Since two forces are pulling on the box, the net force is generally not zero unless the forces are equal and opposite. Without knowing magnitudes, we cannot assume cancellation, so this statement is not generally correct.

Option 2: 'Not enough information' might seem tempting because you don’t have numerical values. However, the fundamental principle is that the acceleration points along the net force regardless of the exact numbers. Even without exact magnitudes, you can still say the acceleration direction aligns with the resultant of the two forces.

Option 3: 'The box will accelerate in the opposite direction of the net force' is inconsistent with Newton's laws. Acceleration occurs in the same direction as the net force, not the opposite.

Option 4: 'The box will accelerate in the direction of the net force' correctly reflects the core idea: the resultant force determines both the acceleration direction and its magnitude (a = F_net / m). The two applied forces combine vectorially, and the box moves in the direction of that combined push or pull.

Option 5: 'The box will accelerate in the direction of the larger force' is a common misconception. If the forces are not collinear or not equal, the net force is not simply the larger one; you must add the vectors to find the true direction of acceleration. Hence this option is misleading unless the forces were strictly along the same line and in the same direction with no other components.

Summarizing the key idea: acceleration is determined by the net force acting on the object, i.e., the vector sum of all applied forces. Therefore, the correct choice is the one stating the box accelerates in the direction of the net force.

In Figure 5.2a (reproduced below), two forces are applied to a box. In which direction will the box accelerate? Single choice

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