Question

student a and student b are pushing a box towards the right by applying force as shown. at the same time, student y and student z are pushing the box with the force shown, but in the opposite direction. student a and student b state that the box will move in the direction of the force that they applied, while student y and student z state that the box will move in the direction that they applied the force. which claim is valid? oa the net force on the box is 7n and the box will move to the left. ob the net force on the box is 4n and the box will move to the right. oc the net force on the box is 11n and the box will move in the direction of the greater force. od the net force on the box is 8n and the box will move in the direction of the lesser force.

Explanation:

Step1: Calculate net force in vertical direction

Forces in vertical direction: \(F_{vertical - down}=5N + 6N=11N\), \(F_{vertical - up}=3N+4N = 7N\). Net vertical force \(F_{vertical - net}=11N - 7N = 4N\) (downward). But since the problem is about horizontal (assuming the direction of student A and B vs Y and Z is horizontal as per the context of net force claim in options). Wait, no, re - check. Wait, the forces are applied as: Student A (5N) and B (6N) in one direction (say negative y - axis if vertical, but the options talk about left/right. Wait, no, misinterpret. Wait, the problem is about net force. The forces: Student A (5N) and B (6N) are in one direction (let's assume downward as per the arrow direction in the figure, but the options are about left/right. No, wait, no, the problem has a mis - label. Wait, no, re - analyze. The forces: Student A (5N) and B (6N) are in one direction (say negative y), Student Y (3N) and Z (4N) in positive y. Net force \(F_{net}=(5 + 6)-(3 + 4)=4N\). But the options are A: 7N left (wrong), B:4N right (wrong as per calculation? No, wait, no, wrong approach. Wait, no, the problem is that the forces are: assume Student A (5N) and B (6N) are in one direction (say negative x - axis, but no, the arrows are vertical. Wait, no, the problem is a mis - print. Wait, no, the correct way: Net force \(F_{net}=(5 + 6)-(3 + 4)=4N\). But looking at the options, option B says net force 4N and move right (if we assume the direction of larger force. Wait, no, the formula for net force when forces are in opposite directions \(F_{net}=F_1 - F_2\) (where \(F_1>F_2\)). Here \(F_1=(5 + 6)=11N\), \(F_2=(3 + 4)=7N\). \(F_{net}=11 - 7=4N\). And the box moves in the direction of the greater force (the direction of Student A and B if we assume their combined force is greater. But the options: Option B: The net force on the box is 4N and the box will move to the right (assuming the direction of Student A and B is right? No, mis - match. Wait, no, re - check the calculation. Wait, no, wrong. Wait, the formula is \(F_{net}=\sum F_{down}-\sum F_{up}\). \(\sum F_{down}=5 + 6=11N\), \(\sum F_{up}=3+4 = 7N\). \(F_{net}=11 - 7=4N\). And the object moves in the direction of the greater force (downward, but the options have right/left. Wait, no, the problem has a typo. Assuming that the direction of Student A and B (5N + 6N) is considered as the direction of net force (if we assume the figure's direction is mis - labeled. If we go by calculation \(F_{net}=4N\) (Option B's net force value matches).

Answer:

B. The net force on the box is 4N and the box will move to the right.