Question

Im so confused also for this gravity is rounded to 10

Answer 1

32cm.

Step-by-step explanation:

Torques would be the easiest way to go about anwsering this question. So lets first define two torques, torque of Carol and torque of Barry, in terms of r.

Define torque as τ=mar, where τ is toruqe, m is mass, a is acceleration, and r is distance from our center of rotation.

∑τ=τcarol+τbarry+τruler

Set a reference point at 50cm, from which we can find the net torque of the ruler with the equation (we can make this assumption since the ruler is uniform):

τruler=mgr where r is the distance from 50cm in meters.

now lets define torqes for each piece in terms of r:

τcarol=mg(r-0.22)

τBarry=mg(r+0.21)

we make the assumption that left is negative and right is positive.

Now we can set up the equation such that:

∑τ=τcarol+τbarry+τruler=mg(r-0.22)+mg(r+0.21)+mgr

Remember, masses aren't equal, so lets set m1=0.013kg, m2=0.019kg, and m3=0.034kg.

`m1*g(r-0.22)+m2*g(r+0.21)+m3*gr\\0.13(r-0.22)+0.19(r+0.21)+0.34r\\0.13r-0.0286+0.19r+0.0399+0.34r\\0.13r+0.0113+0.19r+0.34r\\.66r+0.0113`

all this must equal 0.

0=.66r+0.0113

-0.0113=0.66r

-0.0171=r

since r is displacement from 0.05 m mark, we can assume that the anwser can be negative.

So 17.1 cm to the left of the center, or 32cm.