Answer:
the center of mass is 7.07 cm apart from the bend
Explanation:
the centre of mass of a wire of length L is L/2 ( assuming uniform density). Then initially the x coordinate of the centre of mass is
x₁ = L/2 = 20 cm /2 = 10 cm
when the wire is bent in a right angle the coordinates of the new centre of mass will be
x₂ = L₂/2
y₂= L₂/2
where L₂ is the length of the horizontal piece and vertical piece . Then L₂=L/2
x₂ = L₂/2 = L/4 = 20 cm/4 = 5 cm
y₂= L₂/2 = L/4 = 20 cm/4 = 5 cm
x₂=y₂=X
locating the bend in the origin (0,0) the distance to the centre of mass is
d = √(x₂²+y₂²) = √(2X²) = √2*X=√2*5cm = 7.07 cm
d = 7.07 cm
The bus and the truck have the same velocity.
Also, Valerie and Owen have the same velocity.
<span>These are inert gases, so we can assume they don't react with one another. Because the two gases are also subject to all the same conditions, we can pretend there's only "one" gas, of which we have 0.458+0.713=1.171 moles total. Now we can use PV=nRT to solve for what we want.
The initial temperature and the change in temperature. You can find the initial temperature easily using PV=nRT and the information provided in the question (before Ar is added) and solving for T.
You can use PV=nRT again after Ar is added to solve for T, which will give you the final temperature. The difference between the initial and final temperatures is the change. When you're solving just be careful with the units!
SIDE NOTE: If you want to solve for change in temperature right away, you can do it in one step. Rearrange both PV=nRT equations to solve for T, then subtract the first (initial, i) from the second (final, f):
PiVi=niRTi --> Ti=(PiVi)/(niR)
PfVf=nfRTf --> Tf=(PfVf)/(nfR)
ΔT=Tf-Ti=(PfVf)/(nfR)-(PiVi)/(niR)=(V/R)(Pf/nf-Pi/ni)
In that last step I just made it easier by factoring out the V/R since V and R are the same for the initial and final conditions.</span>
The pet store would be the reference point because it is where he started and it will not move. Hope this helped.
