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
Answer:
The gravitational force between them increases by a factor of 4
Explanation:
Gravitational force is a force of attraction between two objects with masses M and m which are separated by a distance R. It is given mathematically as:
Fg = GMm/R²
Where G = Gravitational constant.
If the distance between their centers, R, decreases by a factor of 2, then it means the new distance between their centers is:
r = R/2
Hence,the gravitational force becomes:
Fg = GMm/r²
Fg = GMm/(R/2)²
Fg = GMm/(R²/4)
Fg = 4GMm/R²
Hence,the gravitational force increases by a factor of 4.
Answer:
1. Battery
2. Copper wire
3. Nail or piece of metal (zinc, iron, or steel).
Answer:
the object will travel 0.66 meters before to stop.
Explanation:
Using the energy conservation theorem:
The work done by the friction force is given by:
![W_f=F_f*d\\W_f=\µ*m*g*d\\W_f=0.35*4*9.81*d\\W_f=13.7d[J]](https://tex.z-dn.net/?f=W_f%3DF_f%2Ad%5C%5CW_f%3D%5C%C2%B5%2Am%2Ag%2Ad%5C%5CW_f%3D0.35%2A4%2A9.81%2Ad%5C%5CW_f%3D13.7d%5BJ%5D)
so:
