A youngster shoots a bottle cap up a 22.0o inclined board at 1.97 m/s. The cap slides in a straight line, slowing to 1.03 m/s after traveling some distance.

Question

If the coefficient of kinetic friction is 0.36, find that distance. 

Answer 1

A youngster shoots a bottle cap up a 22.0o inclined board at 1.97 m/s. The cap slides in a straight line, slowing to 1.03 m/s after traveling some distance.

If the coefficient of kinetic friction is 0.36, find that distance. 

Let D=the unknown distance, then the elevation gained is Dsin22

Initially,

KEi=0.5m(1.97)²=1.94m

PEi=0

Finally,

KEf=0.5m(1.03)²=0.53m

PEf=mgDsin(22)

The work W done by friction is the normal force times the coefficient of friction:

W=0.36mgDcos(22)

Energy Balance

Initial Energy-Work=Final Energy

KEi+PEi-W=KEf+PEf

KEi+0-W=KEf+PEf

1.94m-0.36mgDcos(22)=0.53m+mgDsin(22)

1.94-0.36gDcos(22)=0.53+gDsin(22)

1.94-0.53=gD[sin(22)+0.36cos(22)]

D=(1.94-0.53)/[9.81(0.375+0.36(0.927)]=0.20 m

Note solution does not depend on mass!