38
NEWTON'S LAWS
[CHAP. 3
Fig. 3-11
Writing Fx max , we have Ff from which ax
3.21
0:50mg max
or
51 N
0:50 20 9:81 N 20 kg ax
2:35 m/s2 . The box accelerates down the incline at 2.4 m/s2 .
When a force of 500 N pushes on a 25-kg box as shown in Fig. 3-12, the acceleration of the box up the incline is 0.75 m/s2 . Find the coe cient of kinetic friction between box and incline. The acting forces and their components are shown in Fig. 3-12. Notice how the x- and y-axes are taken. Since the box moves up the incline, the friction force (which always acts to retard the motion) is directed down the incline. Let us ®rst ®nd Ff by writing Fx max . From Fig. 3-12, using sin 408 0:643, 383 N
Ff
0:64 25 9:81 N 25 kg 0:75 m=s2
from which Ff 207 N. We also need FN . Writing Fy may 0, and using cos 408 0:766, we get FN Then
321 N
0:77 25 9:81 N 0 k
Ff 207 0:41 FN 510
Fig. 3-12
or
FN 510 N