# Tension in a string,changing force and equilibrium.s

1. Feb 18, 2012

### uknew

any help is good
so i was thinking about a string and a mass hanging from the center (not tied) of it(any mass "m" and string of negligible mass). so imagine a mass hanging from the center of a string making a "v". and i thought what if i tied one side and pulled horizontally on one side only with a force "f".the mass will move up,so how can i calculate the net acceleration vector. (mag and direction).
my question is mainly about the section of the string that is tied up,..its tension will change as the mass moves up until eventually its equal to the action of the force applied to the other side.
can i use net force =ma? can i use the tension in string that is tied up like it was in equilibrium and add the force applied to that,, plus mg? ifyou dont get the question tell me. there isnt any problem examples like this anywhere. if this question was already answered point it

2. Feb 18, 2012

### zoobyshoe

Interesting question. The side that's tied is going to swing up in an arc, kinda like a sideways pendulum. There's a cool animation of the pendulum acceleration and velocity vectors here:

http://en.wikipedia.org/wiki/Pendulum

In your setup, though, the force causing the swing, unlike gravity, is going to be changing direction and magnitude.

3. Feb 20, 2012

### uknew

yea but in my set up it dont swing it acts more like a simple machine and moves the mass diagonally up ..the applied force on one side is constant and horizontal but the side thats tied is the one that will change(i think) as i pull on one side since the mass hanging from the middle will try to fall because of gravity but the two strings wont let it and the angle will change to eventually 180 degrees(when the weight reaches the top and the "v" set up is now a line) ..eventually the

4. Feb 20, 2012

### zoobyshoe

Maybe I didn't understand the set up. The side that's not tied just goes directly to your hand?

5. Feb 21, 2012

### uknew

oh sory about that.....ok picture a wall,, i get one side of the string and nail it to the wall..then i tie a weight to the middle of the string...now i have nail with string on wall, weight in middle of string and loose end in my hand so as it forms a "v" the part in my hand is pulled horizontally with constant force level with the part tied to the wall so the weight moves up. thats is the set up..my apologies for the lack of description. or picture x and y axis with weight at origin. the strings make angle 1 with x axis positive and angle 2 with x axis negative. ive worked on it and i think that i can assume that force horizontal in the tied side will remain constant(since it wont move to the tied side) and the vertical force in the tied side will decrease as the weight moves up and the vertical and horizontal forces of the string in my hand will be constant, froom that i can calculate ne accel. any takes?

6. Feb 21, 2012

### zoobyshoe

I'm pretty sure it's my fault. I assumed you were going to pass the free end over a nail or peg and pull down a bit to keep the two ends of the string level. Therefore I wrongly assumed the free end of the string would get shorter and shorter as you pulled up. My mistake, because you certainly didn't say you were going to do that.

Well, I found this very set up in two physics texts. Assuming the weight is in the middle of the string, the tension force on both sides will always be equal and opposite. The higher you raise the weight as you move your hand horizontally, however, the greater the tension force will become, and will always exceed the force of the weight itself. (A small weight can put great tension on a stretched string.) The vertical component of the string tension force, will, of course, be equal and opposite to the weight.

You do realize, though, that as the weight is raised it won't move up on a straight diagonal? It will move in an arc. It's at the end of a straight line (the string) that is pivoting around the tied end.

7. Feb 26, 2012

### uknew

thanks, and yea i think the set up you ahad was right, one side is tied and the other end islput over a nail or massless pulley and pulled and the pulled string does get shorteras the mass rises.. so there is no difference between pulling bothsides horizontally with the same force and pulling only one side with a given force? so in free body diagrams i draw two equal forces pulling on a mass at an angle with the horizontal even thogh im actually only pulling on one side? the net acceleratio will be straight up..it cant because that doesnt happen reallly.
my approach was the first law of newton and equilibrium. first i calculated the tensions for the suspended mass in equilibrium t1 and t2, t2 being the tied end. then i applied a force to t1 horizontally so i added this force to horizontal component of t1 and calculated the force for t1 and angle (left the y component as is becuase the force was applied horizontally only) and aded this vecti t1 to t2 and the weight to get a net force. then i got the net accel from that and angle..the first law because an object tends to continue doing what its doing until a force acts on it? im trying to use newtons laws to "predict" the motion of an object..got anywhere with example problms?