Answer:
[ 2.67 , 1 ] m
Explanation:
Given:-
- The side lengths of the rods are as follows:
a = 4 m , b = 4 m , c = 5 m
a = Base , b = Perpendicular , c = Hypotenuse
- All rods are made of same material with uniform density. With
Find:-
Find the coordinates of the center of mass of the triangle.
Solution:-
- The center of mass of any triangle is at the intersection of its medians.
- So let’s say we have a triangle with vertices at points (0,0) , (a,0) , and (0,b).
- Median from (0,0) to midpoint (a/2,b/2) of opposite side has equation:
bx−ay=0
- Median from (a,0) to midpoint (0,b/2) of opposite side has equation:
bx+2ay=ab
- Median from (0,b) to midpoint (a/2,0) of opposite side has equation:
2bx+ay=ab
- Solve all three equations simultaneously:
bx−ay=0 , bx = ay
ay + 2ay = ab , 3ay = ab , y = b/3
bx = b/3
x = a / 3
- So the distance from the median to each leg of the triangle is 1/3 length of other leg.
- So the coordinates of the centroid for right angle triangle would be:
[ 2a/3 , b/3 ]
[ 2.67 , 1 ] m
Apply the combined gas law
PV/T = const.
P = pressure, V = volume, T = temperature, PV/T must stay constant.
Initial PVT values:
P = 1atm, V = 8.0L, T = 20.0°C = 293.15K
Final PVT values:
P = ?, V = 1.0L, T = 10.0°C = 283.15K
Set the PV/T expression for the initial and final PVT values equal to each other and solve for the final P:
1(8.0)/293.15 = P(1.0)/283.15
P = 7.7atm
Answer:
1Mm
Explanation:
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