Question

the diagram below shows three forces acting on a box with a mass of 30kg. diagram: 40n (arrow down), 20n (arrow down), 30n (arrow up), box labeled 30 kg what would be the acceleration rate of the box? options: 3 m/s², 2 m/s², 900 m/s², 1 m/s²

Explanation:

Step1: Calculate net force

First, find the net force acting on the box. The downward forces are \(40N\) and \(20N\), so their sum is \(40 + 20 = 60N\) downward. The upward force is \(30N\). The net force \(F_{net}\) is the difference between downward and upward forces: \(F_{net}=60 - 30 = 30N\) (downward, but magnitude is 30N).

Step2: Apply Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. We know \(F_{net}=30N\) and \(m = 30kg\). Rearranging for \(a\), we get \(a=\frac{F_{net}}{m}\). Substituting the values: \(a=\frac{30}{30}=1m/s^{2}\)? Wait, no, wait. Wait, maybe I messed up the direction. Wait, no, let's recheck. Wait, the downward forces: 40N and 20N, so total downward is 60N. Upward is 30N. So net force is 60 - 30 = 30N downward. Then mass is 30kg. So \(a = F/m = 30/30 = 1m/s^{2}\)? But wait, the options have 2m/s²? Wait, no, maybe I misread the forces. Wait, the diagram: maybe the upward force is different? Wait, no, the problem says three forces: 40N, 20N downward, 30N upward. Wait, 40 + 20 = 60N downward, 30N upward. Net force is 60 - 30 = 30N. Mass 30kg. So \(a = 30/30 = 1m/s²\)? But the options include 2m/s². Wait, maybe I made a mistake. Wait, maybe the upward force is 30N, and the downward forces are 40N and 20N? Wait, no, 40 + 20 is 60, minus 30 is 30. 30N over 30kg is 1m/s². But the options have 1m/s² as an option. Wait, maybe I miscalculated. Wait, let's do it again.

Wait, maybe the forces are: two downward (40N and 20N) and one upward (30N). So net force \(F_{net}=40 + 20 - 30 = 30N\). Then \(a = F_{net}/m = 30/30 = 1m/s²\). So the answer should be 1m/s²? But the options have 3m/s², 2m/s², 900m/s², 1m/s². So 1m/s² is an option. Wait, maybe I messed up. Wait, no, let's check Newton's second law again. \(F = ma\), so \(a = F/m\). Net force is 30N, mass 30kg, so \(a = 1m/s²\). So the correct answer is 1m/s²? Wait, but maybe the diagram is different. Wait, maybe the upward force is 30N, and the two downward forces are 40N and 20N, so net force is 40 + 20 - 30 = 30N. Then 30N / 30kg = 1m/s². So the answer is 1m/s².

Wait, but maybe I misread the mass. The box is 30kg. Yes. So net force is 30N, mass 30kg, acceleration 1m/s². So the correct option is 1m/s².

Answer:

1 m/s² (corresponding to the option "1 m/s²")