Asked by T
A 0.2 kg object is released from rest at point A on a track that is one-quarter of a circle with radius 1.6 m, as shown in the figure. It slides down and reaches point B with a speed of 4.8 m/s. Then it slides on a level surface a distance of 3 m until it comes to rest at point C.
a) How much work is done by friction on the package at it slides down the circular track from A to B?
b) What is the coefficient of kinetic friction on the horizontal surface?
c) What average power is produced by friction as the object moved from B to C?
d) What instantaneous power is produced by friction at point B?
a) How much work is done by friction on the package at it slides down the circular track from A to B?
b) What is the coefficient of kinetic friction on the horizontal surface?
c) What average power is produced by friction as the object moved from B to C?
d) What instantaneous power is produced by friction at point B?
Answers
Answered by
aljmeeli
Ýí ÍÇáÉ ÚÏã ÇáÇÍÊßÇß ÓÊßæä : ÇáØÇÞÉ ÇáßÇãäÉ Ýí ÇáÃÚáì = ÇáØÇÞÉ ÇáÍÑßíÉ Ýí ÇáÃÓÝá ( äåÇíÉ ÇáãäÍÏÑ )
æãÚ æÌæÏ ÇáÇÍÊßÇß Óíßæä ÇáÔÛá åæ ÇáÝÑÞ Èíä ÇáØÇÞÊíä ßÇáÊÇáí :
W=mgh-1/2 mv^2=0.2×9.8×1.6-1/2×0.2×〖4.8〗^2=0.832 J
2.b
áÍÓÇÈ ãÚÇãá ÇáÇÍÊßÇß ÇáÍÑßí äÚÊãÏ Úáì ÇáÌÒÁ Èíä B æ C ßãÇ Ýí ÇáÔßá ÇáãÌÇæÑ ÝÝí åÐå ÇáãäØÞÉ
F_Fric=μ F_n but F_n=mg
F_Fric=μ mg
And
F=ma
a=F/m=(μ mg)/m=μ g
μ=a/g……………..1
So
a=v^2/d=〖4.8〗^2/3=7.68 m/s^2
From ..1
μ=a/g=7.68/9.8=0.78
c.
P ̅=W/t=(F_Fric×d)/t=F_Fric×v ̅
but F_Fric=μ mg=0.78×0.2×9.8=1.53N and v ̅=4.8/2=2.4 m/s
∴ P ̅=F_Fric×v ̅=1.53×2.4=3.67 Watt
d.
P=F_Fric×v=1.53×4.8=7.34 Watt
æãÚ æÌæÏ ÇáÇÍÊßÇß Óíßæä ÇáÔÛá åæ ÇáÝÑÞ Èíä ÇáØÇÞÊíä ßÇáÊÇáí :
W=mgh-1/2 mv^2=0.2×9.8×1.6-1/2×0.2×〖4.8〗^2=0.832 J
2.b
áÍÓÇÈ ãÚÇãá ÇáÇÍÊßÇß ÇáÍÑßí äÚÊãÏ Úáì ÇáÌÒÁ Èíä B æ C ßãÇ Ýí ÇáÔßá ÇáãÌÇæÑ ÝÝí åÐå ÇáãäØÞÉ
F_Fric=μ F_n but F_n=mg
F_Fric=μ mg
And
F=ma
a=F/m=(μ mg)/m=μ g
μ=a/g……………..1
So
a=v^2/d=〖4.8〗^2/3=7.68 m/s^2
From ..1
μ=a/g=7.68/9.8=0.78
c.
P ̅=W/t=(F_Fric×d)/t=F_Fric×v ̅
but F_Fric=μ mg=0.78×0.2×9.8=1.53N and v ̅=4.8/2=2.4 m/s
∴ P ̅=F_Fric×v ̅=1.53×2.4=3.67 Watt
d.
P=F_Fric×v=1.53×4.8=7.34 Watt
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.