Vector magnitude on an inclined plane - should be a quick answer

[tlonster]

Homework Statement

Please see attachment.

When θ = 0, mass m is at the bottom of the inclined plane.

If I create a frame at origin O, with axes along the bottom of the plane and the dotted line (as shown in the picture), will my magnitude of the vector from O to A (along the dotted line) just be "l" (length of string)?

Homework Equations

No equations

The Attempt at a Solution

I feel like it is l + some other distance that I have no idea how to get. How I read the question is that the ball is at the edge of plane at θ=0, so that magnitude should be l + diameter of the mass. I'm not given any dimensions, or where point A is located. Is the magnitude just the length of the string and it's a poor drawing?

 

[Simon Bridge]

If I create a frame at origin O, with axes along the bottom of the plane and the dotted line (as shown in the picture), will my magnitude of the vector from O to A (along the dotted line) just be "l" (length of string)?

Not in general. If it were then the pendulum would just hit the bottom of the ramp and stick instead of oscillating like you want it to do.

However - the description appears to be saying that the mass is to be treated as a point mass and it just sweeps past the bottom of the ramp at zero angle without being impeded. Unless you have a number for the radius of the mass?

 

[tlonster]

I don't have any dimensions. I'm asked to find the equation of motion of the point mass, so it's actually very involved (have three reference frames now). Maybe it ends up dropping out once I get everything set up. Should I just call that distance vector "D" for now and see what happens?

 

[tlonster]

*distance vector magnitude "D"

 

[Simon Bridge]

Hint: resolve all vectors to the plane of the ramp and use that as your single reference frame. The only force not in the plane of the ramp is gravity.