In Fig. 5-21, forces${\overrightarrow{\mathbf{F}}}_{\mathbf{1}}$and${\overrightarrow{\mathbf{F}}}_{\mathbf{2}}$are applied to a lunchbox as it slides at constant velocity over a frictionless floor. We are to decrease angle$\mathit{\theta }$without changing the magnitude of${\overrightarrow{\mathbf{F}}}_{\mathbf{1}}$. For constant velocity, should we increase, decrease, or maintain the magnitude of${\overrightarrow{\mathbf{F}}}_{\mathbf{2}}$?

It is given that the object is moving with constant velocity, so the net force acting on it would be zero.

The problem is based on Newton’s second law of motion. The law states that the acceleration of an object is dependent on the net force acting upon the object and the mass of the object. Also, it involves the resolution of vectors. Here, the forces can be resolved to find the net force. Net force can be found using Newton’s law of motion. By writing down the equation for the net force, the relationship between the forces and the angle can be found.

Here,we have to use Newton’s second law. As velocity is constant, the net force is

${\mathrm{F}}_{\mathrm{net}}=0$

So-net force is as follows,

role="math" localid="1657003263144" $$\begin{gathered} {\mathrm{F}}_2-{\mathrm{F}}_1\cos \mathrm{\theta }=0 \\ {\mathrm{F}}_2={\mathrm{F}}_1\mathrm{cos\theta } \\ {\mathrm{F}}_1=\frac{{\mathrm{F}}_2}{\mathrm{cos\theta }} \end{gathered}$$

Here we have to decrease role="math" localid="1657003321674" $\mathrm{\theta }$by keeping the value of ${\mathrm{F}}_1$constant, so ${\mathrm{F}}_2$must be increased