Question

Determine the applied force (in newtons, N) required to accelerate a 3.46-kg object rightward with a constant acceleration of 1.86 m/s^2 if the force of friction opposing the motion is 16.4 N.

Answer 1

Step-by-step explanation

The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

`\begin{gathered} F=ma \\ where\text{ F is the force} \\ a\text{ is the acceleration} \\ m\text{ is the mass} \end{gathered}`

Step 1

Free body diagram

so

the sum of force in x direction

`\begin{gathered} sum\text{ of forces=required force-force of friction} \\ replace \\ sum=required\text{ force-16.4 N} \end{gathered}`

now, replace in the formula

`\begin{gathered} F=ma \\ required\text{ force-16.4 N=3.46 kg*1.86}(m)/(s^2) \\ required\text{ force-16.4 N=6.4354 N} \\ add\text{ 16.4 N in both sides} \\ requ\imaginaryI red\text{force-16.4N+16.4 N=6.435,4N+16.4 N} \\ requ\mathrm{i}red\text{ force=22.83 N} \end{gathered}`

therefore, the required force is 22.83 N

I hope this helps you