Learning Goal: To practice Problem-Solving Strategy 6.2 for dynamics problems. A

Question

Learning Goal: To practice Problem-Solving Strategy 6.2 for dynamics problems. A box of mass 3.06 kg slides down a rough vertical wall. The gravitational force on the box is 30 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 = 23 N , as shown in (Figure 1) . There is now a frictional force between the box and the wall of magnitude 13 N . How fast is the box sliding 3.0 s after you started pushing on it?

Explanation / Answer

How fast after 3.0 secs:
Sum of Forces in X direction = n - Fpx =0
n=Fpx
Sum of forces in y direction = ff-fg + Fpy
ff = frictional force
fg= force due to gravity
n= normal force
Fp= force of push

Fp= 23 what about Fpy and Fpx
Draw a triangle with an angle of 135 and the hypotonus is 23 so Fpy= sin135*23
Fpx= cos135*23
solve for a from the sum of forces in y direction
F in y direction= 13-30+16.3 = -.7
-.7 =ma -.7=3.06a
a=-.2288

solve for final v
vf=vi +at
vf= -2.5 + (-.2288)3
vf= 3.18 m/s

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