Question

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${\overrightarrow{\mathbf{F}}}_{\mathbf{2}}$?

Short answer

We should increase the magnitude in the angle on Force${\mathrm{F}}_2$ for constant velocity

Step-by-step solution

Given information

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

To understand the concept

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.

To find whether we should increase or decrease or maintain the magnitude in the angle on Force F2 for constant velocity

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