Calculating Pendulum Length with Given Velocity and Tension

[WadeS]

Conservative Forces and Potential Energy

Homework Statement

A mass hangs on the end of a massless rope. The pendulum is held horizontal and released from rest. When the mass reaches the bottom of its path it is moving at a speed v = 2.1 m/s and the tension in the rope is T = 19.3 N.

1)
How long is the rope?

So we know that the velocity at the bottom is 2.1m/s, and the T is 19.3, we are looking for the length of the rope, L

Homework Equations

I was using v=square root of (gl)

then tried using : v^2= 2gL

none of which gave my the correct answer

The Attempt at a Solution

2.1^2=2(9.81)L
L=2.1^2/2(9.81)= .22 m

if anyone can provide a clarification for this, it is a simple problem which I should be able to figure out but whether I am using the wrong equation or simply plugging it in wrong , I am unsure. Any help and guidance is much appreciated!

Regards,

 

[jedishrfu]

Are you sure the T is the tension on the rope or is it instead the period of the pendulum?

 

[PhanthomJay]

Homework Statement

A mass hangs on the end of a massless rope. The pendulum is held horizontal and released from rest. When the mass reaches the bottom of its path it is moving at a speed v = 2.1 m/s and the tension in the rope is T = 19.3 N.

1)
How long is the rope?

So we know that the velocity at the bottom is 2.1m/s, and the T is 19.3, we are looking for the length of the rope, L

Homework Equations

I was using v=square root of (gl)

then tried using : v^2= 2gL

none of which gave my the correct answer

The Attempt at a Solution

2.1^2=2(9.81)L
L=2.1^2/2(9.81)= .22 m

if anyone can provide a clarification for this, it is a simple problem which I should be able to figure out but whether I am using the wrong equation or simply plugging it in wrong , I am unsure. Any help and guidance is much appreciated!

Regards,

You should not blindly choose equations and hope that one of them works. Equations are not laws.
Total Energy is always conserved. Try the Conservation of Energy Law to see if your answer is correct. It might be, but you won't know for sure until you start from basic principles.

 

[WadeS]

Are you sure the T is the tension on the rope or is it instead the period of the pendulum?

Yes, T is the tension on the rope :)

 

[WadeS]

You should not blindly choose equations and hope that one of them works. Equations are not laws.
Total Energy is always conserved. Try the Conservation of Energy Law to see if your answer is correct. It might be, but you won't know for sure until you start from basic principles.

1/2mv^2=mgh -->1/2v^2=gh
Which then isolates to h =1/2v^2/g

That was actually the first thing I tried but I still didn't get the right answer which lead me to think I was using the wrong equation so I used a different one

 

[PhanthomJay]

1/2mv^2=mgh -->1/2v^2=gh
Which then isolates to h =1/2v^2/g

That was actually the first thing I tried but I still didn't get the right answer which lead me to think I was using the wrong equation so I used a different one

Your method and answer is correct. I don't know why someone or some thing is telling you differently.

 

[WadeS]

Your method and answer is correct. I don't know why someone or some thing is telling you differently.

Exactly why I'm baffled.. It's an online homework system so it immediately tells me if I did it right or wrong..

 

[jedishrfu]

Exactly why I'm baffled.. It's an online homework system so it immediately tells me if I did it right or wrong..

Some of these systems are very picky. My son had some high school chemistry homework to do. The training system the teacher selected came from UT and was geared toward the specific periodic table in his chemistry book. We did several problems but used another periodic table which had some atomic weights off by hundredths and his answers would keep getting rejected until we used the right periodic table. I think the tolerance is often set too high on these tutoring systems.

 

[WadeS]

Some of these systems are very picky. My son had some high school chemistry homework to do. The training system the teacher selected came from UT and was geared toward the specific periodic table in his chemistry book. We did several problems but used another periodic table which had some atomic weights off by hundredths and his answers would keep getting rejected until we used the right periodic table. I think the tolerance is often set too high on these tutoring systems.

Yeah! I kept putting in two decimal places but it didn't take my answer until I put in 3... It gets frustrating to say the least, but thank you both! :)