Isabella pushes a box of mass 5.25 kilograms with a force of 15.7 newtons, it accelerates by a rate of 2.50 meters/second². What is the force due to friction in this scenario?

Steps to Solve

1. Identify Given Values We have the following information:

   • Mass of the box, $m = 5.25 \text{ kg}$
   • Applied force, $F_{applied} = 15.7 \text{ N}$
   • Acceleration, $a = 2.50 \text{ m/s}^2$

2. Calculate the Force of Friction We can use Newton's Second Law of Motion which states that the net force is equal to mass times acceleration. The equation for net force is:

   $$ F_{net} = m \cdot a $$

   Substituting in the values we have:

   $$ F_{net} = 5.25 \text{ kg} \cdot 2.50 \text{ m/s}^2 $$

3. Calculate the Value of $F_{net}$ Now we perform the calculation:

   $$ F_{net} = 5.25 \cdot 2.50 = 13.125 \text{ N} $$

4. Determine the Force of Friction The net force can also be calculated as the applied force minus the force of friction. Thus, we can rearrange the equation:

   $$ F_{friction} = F_{applied} - F_{net} $$

   Substituting in the values:

   $$ F_{friction} = 15.7 \text{ N} - 13.125 \text{ N} $$

5. Calculate the Force of Friction Now we perform this final calculation:

   $$ F_{friction} = 15.7 - 13.125 = 2.575 \text{ N} $$

   Since we are asked for the force due to friction, we will report this as negative because it opposes the direction of the applied force:

   $$ F_{friction} = -2.575 \text{ N} $$