Rigid Body Problem

Bucky

1. Homework Statement

Uniform disc, mass m, falls from position where theta 60 degrees. (P is a fixed point on rim of disc).

Calculate the components of thrust along and perpendicular to GP on the smooth hinge at P when theta = 30degrees.

see attatched image for diagram

2. Homework Equations

3. The Attempt at a Solution

NB: theta with a dot is velocity (v), and theta with two dots is acceleration (r). Not sure if these are actually what the two of them mean, but thats what they'll be represented by.

Transverse Equation:

-ma(r)= mg sin theta - x
x = mgsin theta + ma(r) (1)

ma (v)^2= y - mgcos theta
Y = ma (v)^2+ mgcos theta (2)

Rotational equation about P

I r= sum of moments
2/3 m(a)^2 r= -mgasin theta

2/3a r= -g sin theta

a r= -(3/2) g sin theta (3)

Integrating (3) gives

a r= -3/2g cos theta + c

c = 3/2g cos theta

at theta = 60

c = 3/2g cos 60
therefore
c = 3/4 g

so

a (v)^2= -3/2g cos theta + 3/4 g

at theta = 30, (3) gives

a r= -3/2g sin30
= -3/4g

(4) gives

a (v)^2= -3/2g cos30 + 3/4g
= -3/2 * root(3)/2g + 3/4g
= -3root(3)/4g + 3/4g

= (3-3root(3))/4 g

From (3), at theta = 60

-ma r= mgsin theta - x
-m(-g/3) = mgsin60 - x
1/3mg = root(3)/2mg - x
1/3mg = root(3)/2mg - x
2/6mg = 3root(3)/6mg - x
x = 3root(3) - 2/6 mg

which is wrong. So I won't even bother looking at my value for y...

And i'm not sure where i've went wrong :/ seems every time i attempt this question I get a different answer.

Attachments

• 8.8 KB Views: 358
Related Introductory Physics Homework Help News on Phys.org

"Rigid Body Problem"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving