A trapdoor on a stage has a mass of 20.8 kg and a width of 1.58 m (hinge side to handle side). The door can be treated as having uniform thickness and density. A small handle on the door is 1.41 m away from the hinge side. A rope is tied to the handle and used to raise the door. At one instant, the rope is horizontal, and the trapdoor has been partly opened so that the handle is 1.13 m above the floor. What is the tension, T, in the rope at this time?
I know the answer is 85.3 N, but how do I arrive at this answer? Thank you in advance.
Draw a free-body diagram of the trap door and put in all the forces in the proper directions.
Since the hinge reaction is usually not known, you can eliminate it by taking moments about the hinge.
Post if you can use more help.
85.3N is correct.
Do not forget that the angle θ of the door with the horizontal is equal to
sqrt(1-(1.13/1.41)²)=0.5981 (approx.)
When I try balancing the forces, I end up with T = mg, which gives me an answer which is over twice the correct answer.
I'm also confused as to why the angle θ is 0.5981. I thought I had to use
arctan(1.13/141) which gives me a 38.9 degree angle.
Sorry, what I meant was cos(θ) is 0.5981.
The cosine is necessary to calculate the horizontal distance of the centroid of the trap door from the hinge, i.e.
D=(width/2)*cos(θ)
So moment = mg*D
The opposing moment is T*vertical distance
=T*1.13
You can then solve for T (in newtons)
Now I'm getting over 1000. However, I may be reading your explanation wrong. I'll reread your explanation again.
Sorry I let my friend use my laptop and he must have typed in his into Jiskha. It's still Tim. Sorry for the confusion.
Did you solve:
1.13T=mg(W/2)cos(θ)
for T?
Yes. However, I think I hit a wrong number on my calculator before. I still get around 142.6, though.
Does θ equal 0.5981 degree and W equal 1.58 m?
This is what I'm doing to solve for tension:
1) 1.13T=mg(W/2)cos(θ)
2) 1.13T=(20.8)(9.81) x (1.58/2cos(0.5981))
3) 1.13T= 1.61.1891373
4) T= 142.6452543 = 143 N
Am I calculating something wrong? Am I solving for the wrong units?