Wave travel time on string supporting a block on incline

[jwbehm]

Homework Statement

A block of mass 3.1 kg rests on a frictionless inclined plane, held in place by a string of mass 0.023 kg. The angle of the plane from the horizontal is 32°, and the string length is 1.5 m. How long does it take a wave to travel from one end of the string to the other? Note: Since the string is so much less massive than the block, the mass of the string can be neglected when calculating its tension.

Homework Equations

v= square root of F/linear density
v= Distance/Time

The Attempt at a Solution

I have worked this several times and I keep coming up with .025. I got force of gravity in the x direction and came up with 55.1N. I then divided that by the linear density (.023/1.5m.) After taking the square root of that, my V was 59.9 M/s. I then put that in the V= D/T and got .025. Please tell me where I'm going wrong here. Thanks!

 

[Doc Al]

I got force of gravity in the x direction and came up with 55.1N.

Show how you got that.

 

[jwbehm]

30.38/sin32

 

[Doc Al]

30.38/sin32

That's incorrect. You need to review how to find the component of weight parallel to the incline.

 

[jwbehm]

ahhh i knew it would be something stupid like that! Ill look into it and get back on here. Thanks

 

[jwbehm]

Hmm still confused. I think I am getting the angles in the wrong places. Is it Fgx= 30.38/cos32?

Edit

I don't think that's right. . . i don't know where I'm going wrong

 

[jwbehm]

 

[jwbehm]

Figured it out. Thanks for the help

 

[Doc Al]

Figured it out. Thanks for the help

I'm glad you figured it out. In your diagram, you have the x-component as the hypotenuse of your right triangle. That's incorrect. The hypotenuse is always the full vector, which in this case is Fg; the components are the smaller sides.