Question

1. two men try to move a 100 kg box on a frictionless surface, one man pushes to the right with a force of 150 n, and the other pushes to the left with 200 n

a. draw a free body diagram for the box.
b. calculate the net force on the box.
c. find the acceleration of the box.

Explanation:

Step1: Determine net force

Net force \(F_{net}\) is calculated by subtracting forces in opposite directions. Let left - direction be negative and right - direction be positive. \(F_{1}=150N\) (right), \(F_{2}=- 200N\) (left). \(F_{net}=F_{1}+F_{2}=150+( - 200)=-50N\) (negative sign indicates left - direction).

Step2: Calculate acceleration

Using Newton's second law \(F = ma\), where \(m = 100kg\) and \(F=-50N\). Rearranging for \(a\), we get \(a=\frac{F}{m}\). Substitute values: \(a=\frac{-50}{100}=-0.5m/s^{2}\) (negative sign indicates acceleration is to the left).

Answer:

b. The net force on the box is \(50N\) to the left.
c. The acceleration of the box is \(0.5m/s^{2}\) to the left.

For part a (free - body diagram):

• Draw a rectangle to represent the box.
• Draw a vertical upward arrow labeled \(F_N\) (normal force, magnitude \(F_N = mg=100\times9.8 = 980N\)).
• Draw a vertical downward arrow labeled \(F_g\) (force of gravity, \(F_g = 980N\)).
• Draw a horizontal right - ward arrow labeled \(150N\).
• Draw a horizontal left - ward arrow labeled \(200N\).