AP PROBLEM CHILD ON A SWING
AN ADULT EXERTS A HORIZONTAL FORCE ON A SWING THAT IS SUSPENDED BY A ROPE OF LENGTH L, HOLDING IT AN AN ANGLE q WITH THE VERTICAL. THE CHILD IN THE WING HAS WEIGHT W AND DIMENSIONS THAT ARE NEGLIGIBLE COMPARED TO L. THE WEIGHTS OF THE ROPE AND OF THE SEAT ARE NEGLIGIBLE. IN TERMS OF W AND q DETERMINE
A) THE TENSION IN THE ROPE
B) THE HORIZONTAL FORCE EXERTED BY THE ADULT
THE ADULT RELEASE THE SWING FROM REST. IN TERMS OF W AND q, DETERMINE
C) THE TENSION IN THE ROPE JUST AFTER THE RELEASE (THE SWING IS INSTANTANEOUSLY AT REST)
D) THE TENSION IN THE ROPE AS THE SWING PASSES THROUGH IS LOWEST POINT
3 answers
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A) T = W/cos(q) (b/c Tcos(q) = W)
B) F = W*tan(q) (b/c F = Tsin(q)
C) T = W*cos(q) (Find T so that acceleration is tangential to the circle)
D) Not sure but if you want it in terms of W and q I used potential and kinetic energy in terms of L and then plugged it into my equation T = W + (W/10)(v^2/L). The L's cancel and I came up with T = W + 2W*cos(q). (note: i used g = 10 m/s^2)
B) F = W*tan(q) (b/c F = Tsin(q)
C) T = W*cos(q) (Find T so that acceleration is tangential to the circle)
D) Not sure but if you want it in terms of W and q I used potential and kinetic energy in terms of L and then plugged it into my equation T = W + (W/10)(v^2/L). The L's cancel and I came up with T = W + 2W*cos(q). (note: i used g = 10 m/s^2)
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1 answer