Performer Grips
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Please help with this Physics Question!?
A 50 kg circus performer grips a vertical rope with her teeth and sets herself moving in a circle with a radius of 5.0m at a constant horizontal speed of 3.0 ms-1.
(A) What angle does the rope make the vertical?
(B) What is the magnitude of the tension in the rope?
(A) The only force acting horizontally is the horizontal component of tension which causes a centripetal acceleration. From Newton's 2nd law :
∑F = mc(c) = Tsinθ
But centripetal acceleration, a(c) is equal to v² / r, so this equation becomes :
m v² / r = Tsinθ--------> equation (1)
The vertical forces acting on the performer are the performer's weight and the vertical component of tension :
∑F = 0 = Tcosθ – mg
mg = Tcosθ-------> equation (2)
By dividing (1) by (2) we can obtain the trig identity tan = sin / cos, eliminate T, and solve for the angle :
m v² / r / mg = Tsinθ / Tcosθ
tanθ = v² / gr
θ = tanˉ¹( v² / gr)
= tanˉ¹[(3.0m/s)² / (9.8m/s² x 5.0m)]
= 10° (rounded)
(B) From (2) :
mg = Tcosθ
T = mg / cosθ
= (50kg)(9.8m/s²) / cos10°
= 498N
Hope this helps.
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Performer Grips
Performer Grips