Question

1. thomas pushes a 250 - n box across a wooden floor using 75 n of force. if a second box of the same weight is stacked on top of the first, how much force would thomas need to push the two boxes across the same floor?

Explanation:

Step1: Determine the relationship between force and weight

The force \(F\) needed to push an object is related to the normal force \(N\) (which is equal to the weight \(W\) of the object on a horizontal surface) by \(F = \mu N\), where \(\mu\) is the coefficient of friction. For the first box, \(F_1=\mu W_1\), given \(F_1 = 75\space N\) and \(W_1=250\space N\).

Step2: Calculate the force for two boxes

When a second box of the same weight is stacked, \(W_2 = 2W_1=2\times250 = 500\space N\). Since \(F=\mu N\) and \(\mu\) remains the same (same floor), and \(F_1=\mu W_1\), \(F_2=\mu W_2\). Substituting \(W_2 = 2W_1\) into \(F_2=\mu W_2\), we get \(F_2 = 2\mu W_1\). But since \(F_1=\mu W_1 = 75\space N\), then \(F_2=2F_1\).

Answer:

\(150\space N\)