Question

A box of mass 3.0 kg slides down a rough vertical wall. The gravitational force on the box is 29.4 N·When the box reaches a speed of 2.5 m/s you start pushing on one edge of the box at a 45° angle (use degrees in your calculations throughout this problem) with a constant force of magnitude Fp 230 N, as shown in (Figure 1). There is now a frictional force between the box and the wall of magnitude 13.0 N How fast is the box sliding 2.0 s after you started pushing on it?

Answer 1

Given:

Mass: $3.0kg$  

Gravitational force:$29.4 N$

Speed: $2.5 m/s$  

Angle: $45^\circ$  

Force of magnitude:$23.0 N$  

Wall of magnitude:$13.0 N$  

To find:

How fast is the box sliding  $2.0 s$ after you started pushing on it

Step by step Explanation:

Since I don't have a figure, I'll assume the applied force is at a $45$ -degree upward angle.  

speed of origin:  $2.5m/sec^2$  

UP component of applied force  $=(\sin45\times23)$

                                                       $=16.263N$

You then produce $13N$ frictional force.  

Total force acting upwards

$=16.263+13$

$=29.263$                                                

The box's total weight is $(3.1\times g)=30.38N$

Net accelerating force now operating

$=(30.38-29.263)$

$=1.117N$  

The acceleration is still positive  

Acceleration $=(\frac fm)$  

                      $=(\frac{1.117}{3.1})$      

                      $=0.36m/sec^2$

After $2$ secs,  

the box has gained$=(0.36\times2)$

                                $=0.72m/sec$

Final speed after $2$ secs,

                               $=(2.5+0.72)$

                               $=3.22m/sec$