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
Start with 2,000 grams.
After 1 half-life, 1,000 grams are left.
After another half-life, 500 are left.
After another half-life, 250 are left.
After another half-life, 125 are left.
That was FOUR half-lifes.
X = 4 .
Answer:
Motion with constant velocity of magnitude 1 m/s (uniform motion) for 4 seconds in a positive direction and then for 2 seconds uniform motion with constant velocity of magnitude 3 m/s in reverse direction .
Explanation:
The graph shows a constant velocity of 1 m/s for 4 seconds in the positive direction. After that, between 4 seconds and 6 seconds, the object reverses its motion with constant velocity of magnitude 3m/s.
Answer:
450 kJ
Explanation:
Q = mCΔT
where Q is heat (energy),
m is mass,
C is specific heat capacity,
and ΔT is the temperature change.
Q = (1.2 kg) (4180 J/kg/°C) (100°C − 10°C)
Q = 451,440 J
Q ≈ 450 kJ
Answer:
1/2
Explanation:
The energy stored in a capacitor is given by
where
C is the capacitance
V is the potential difference
Calling 
the capacitance of capacitor 1 and 
its potential difference, the energy stored in capacitor 1 is
For capacitor 2, we have:
- The capacitance is half that of capacitor 1: 
- The voltage is twice the voltage of capacitor 1: 
so the energy stored in capacitor 2 is
So the ratio between the two energies is
