If vector b is added to vector a under what conditions does the resultant vector has magnitude a+b?
2 answers:
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5)
In physics, forces are interactions that are able to change the velocity of an object.
Force is a vector quantity, so it has a magnitude and a direction.
The SI units of the force is the Newton (N).
Whenever an unbalanced force is applied to an object, the object experiences an acceleration, according to Newton's second law of motion:
where
F is the force
m is the mass of the object
a is its acceleration
So, the acceleration of an object is proportional to the force applied:
6)
In physics, arrows are used to represent vector quantities. Therefore, they are also used to represent forces.
In particular, when a vector quantity is represented by an arrowr:
- The length of the arrow is proportional to the magnitude of the vector quantity
- The direction of the arrow corresponds to the direction of the vector quantity
Therefore, if a force is represented through an arrow:
- The length of the arrow shows the strength (magnitude) of the force
- The direction of the arrow shows the direction of the force
7)
As we said in part 5), the SI units of the force is the Newton (N).
We can rewrite the Newton in terms of fundamental units only. We can do it starting from the equation:
where
F is the force
m is the mass
a is the acceleration
- The mass is measured in kilograms (kg)
- The acceleration is measured in meters per second squared ()
Therefore, 1 N corresponds to:
B)
Gravity is an attractive force that exists between all objects that have mass. See more explanations about gravity in part 4).
3)
Mass is a scalar quantity; it gives us a measure of the "amount of matter" contained in an object.
The SI unit of the mass is the kilogram (kg).
Being a scalar, mass has no direction, but only a magnitude.
Moreover, the mass is an intrinsec property of an object: therefore, it does not depend on the location of the object. So, an object has always the same mass, either it is on Earth or on another planet.
On the other hand, the force of gravity on an object depends on its location, so it changes.
4)
As we said in part 3), gravity is an attractive force that exists between all objects that have mass.
The magnitude of the force of gravity between two objects is given by the Universal Law of gravitation:
where
G is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between the objects
From the equation above, we observe that:
- all objects are attracted to one another with a gravitational force that is proportional to the mass of the objects and inversely proportional to the square of the distance between them.
And so:
a. When the mass of one or both objects increases, the gravitational force between the objects increases
b. When the distance between two objects increases, the attraction between the objects decreases