Answer: ![F_{2}=\frac{3}{4}F_{1}](https://tex.z-dn.net/?f=F_%7B2%7D%3D%5Cfrac%7B3%7D%7B4%7DF_%7B1%7D)
Explanation:
According to Newton's law of universal gravitation:
Where:
is the module of the force exerted between both bodies
is the universal gravitation constant.
and
are the masses of both bodies.
is the distance between both bodies
In this case we have two situations:
1) Two bags with masses
and
mutually exerting a gravitational attraction
on each other:
(1)
(2)
(3)
2) Two bags with masses
and
mutually exerting a gravitational attraction
on each other (assuming the distance between both bags is the same as situation 1):
(4)
(5)
(6)
Now, if we isolate
from (3):
(7)
Substituting
found in (7) in (6):
(8)
(9)
Simplifying, we finally get the expression for
in terms of
:
The distance covered by car is equal to (assuming it is moving by uniform motion) the product between the car's speed and the time of the car ride, 4 h:
![S_c = v_c t_c](https://tex.z-dn.net/?f=S_c%20%3D%20v_c%20t_c%20)
where
![v_c](https://tex.z-dn.net/?f=v_c%20)
is the car's speed
![t_c = 4 h](https://tex.z-dn.net/?f=t_c%20%3D%204%20h)
is the duration of the car ride
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
![S_t = v_t t_t](https://tex.z-dn.net/?f=S_t%20%3D%20v_t%20t_t)
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
![S=255 km = S_c + S_t](https://tex.z-dn.net/?f=S%3D255%20km%20%3D%20S_c%20%2B%20S_t%20)
which becomes
![255 = 4 v_c + 7 v_t](https://tex.z-dn.net/?f=255%20%3D%204%20v_c%20%2B%207%20v_t)
(1)
we also know that the train speed is 5 km/h greater than the car's speed:
![v_t = 5 + v_c](https://tex.z-dn.net/?f=v_t%20%3D%205%20%2B%20v_c)
(2)
If we put (2) into (1), we find
![255 = 4v_c + 7(5+v_c)](https://tex.z-dn.net/?f=255%20%3D%204v_c%20%2B%207%285%2Bv_c%29)
and if we solve it, we find
![v_c = 20 km/h](https://tex.z-dn.net/?f=v_c%20%3D%2020%20km%2Fh)
![v_t = 25 km/h](https://tex.z-dn.net/?f=v_t%20%3D%2025%20km%2Fh)
So, the car speed is 20 km/h and the train speed is 25 km/h.
Answer: Stationary or constant velocity
Explanation:
Objects with balanced forces acting on them experience no change in motion, or no acceleration. So these objects could either be stationary at rest or have a constant velocity. These include a hanging object, a floating object, an object on a table that doesn't move, and a car moving at a constant 10 mph
Answer:
C. It is radiation leftover from the Big Bang
Answer:
C. Count the atoms in each substance in the reactants and products.
Explanation:
A chemical reaction can be defined as a chemical process which typically involves the transformation or rearrangement of the atomic, ionic or molecular structure of an element through the breakdown and formation of chemical bonds to produce a new compound or substance.
In order for a chemical equation to be balanced, the condition which must be met is that the number of atoms in the reactants equals the number of atoms in the products.
This ultimately implies that, the mass and charge of the chemical equation are both balanced properly.
In Chemistry, all chemical equation must follow or be in accordance with the Law of Conservation of Mass, which states that mass can neither be created nor destroyed by either a physical transformation or a chemical reaction but transformed from one form to another in an isolated (closed) system.
One of the step used for balancing chemical equations is to count the atoms in each substance in the reactants and products.
For example;
NH3 + O2 -----> NO + H2O
The number of atoms in each chemical element are;
For the reactant side:
Nitrogen, N = 1
Hydrogen, H = 3
Oxygen, O = 2
For the product side;
Nitrogen, N = 1
Hydrogen, H = 2
Oxygen, O = 2
When we balance the chemical equation, we would have;
NH3 + 3O2 -----> 4NO + 2H2O