Almost as consistent as Earth’s gravitational force is Colgate’s tradition of putting on “This is Not a Play About Sex”. The play serves to put into dialogue many difficult topics regarding sexual assault, identity, intimacy, relationships, and consent. With the show running this weekend, I took time out of studying for physics and made my way down to Brehmer Theater, hoping to enjoy an hour or so free of all things physics. Much to my dismay (or should I say liking?), I learned that even Colgate’s dark auditorium abounds with all things physics! From the second they drew the curtains to the moment they closed them, I was thinking all about the force of tension, gravity, and pulleys. So what better way to express my thoughts about physics, than blog about them!
The drawing of the curtains could even stir a gasp of anticipation from Isaac Newton himself, however, instead of looking forward to the play, he might be marveling at the physics of this first act. I too, found myself wondering about the force of tension required to open the curtains. Since I do not know enough about modern curtain pulling systems, I’ll make the assumption that the curtain is being pulled by a person standing off stage who is pulling a rope that is attached to the top corner of the fabric at a 30 degree angle with his or her torso. I will also assume that the top of the fabric from the curtain is attached to an aluminum frame that slides along a steel platform (giving it a static friction coefficient of 0.61) and the stage curtain weighs approximately 300 lbs (136 kg). My question is what force of tension is required to begin drawing the curtain?
The free body diagram reveals that in the y direction, there are three forces: normal, gravitational, and a component of tension. In the x, there is friction and the x component of tension. Since we are analyzing the instantaneous moment before the curtain moves and there is no vertical movement, acceleration is equal to 0 m/s^2. We then rearrange the equations and solve for the force of tension (as shown in the picture). It turns out the force required to pull the curtain is equal to about 1450 Newton’s. To put this value in perspective, that is the force required to lift about 325 lbs.
This value leads me to believe there are most likely different mechanics at play (perhaps a pulley or some kind of electrical support). The only thing I know for certain is that I know nothing about stage curtains. And unlucky for me, this is NOT a play about stage curtains!
ΣFy: Fn-mg-Ftsin30=0 ΣFx: Ftcos30-ʯsFn=0