explain newtons second law of motion and derive the formula
Answers
Answer:
According to Newton's second Law of motion the rate of change of linear momentum is directly proportional to the force applied on the body.
Class 11
F = k dp
dt
F = d(mv) k=1
dt
F = mdv
dt
F = ma
Or
Class 9
F = k (mv-mu)
t
F = k m (v-u)
t
F = kma
F = ma k=1
Answer:
Newton's second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In equation form, Newton's second law of motion is a=Fnetm a = F net m.
Newton’s Second Law of Motion: Concept of a System.
in velocity. A change in velocity means, by definition, that there is an acceleration. Newton’s first law says that a net external force causes a change in motion; thus, we see that a net external force causes acceleration.
Another question immediately arises. What do we mean by an external force? An intuitive notion of external is correct—an external force acts from outside the system of interest. For example, in Figure 1(a) the system of interest is the wagon plus the child in it. The two forces exerted by the other children are external forces. An internal force acts between elements of the system. Again looking at Figure 1(a), the force the child in the wagon exerts to hang onto the wagon is an internal force between elements of the system of interest. Only external forces affect the motion of a system, according to Newton’s first law. (The internal forces actually cancel, as we shall see in the next section.) You must define the boundaries of the system before you can determine which forces are external. Sometimes the system is obvious, whereas other times identifying the boundaries of a system is more subtle. The concept of a system is fundamental to many areas of physics, as is the correct application of Newton’s laws. This concept will be revisited many times on our journey through physics.
(a) A basketball player pushes the ball with the force shown by a vector F toward the right and an acceleration a-one represented by an arrow toward the right. M sub one is the mass of the ball. (b) The same basketball player is pushing a car with the same force, represented by the vector F towards the right, resulting in an acceleration shown by a vector a toward the right. The mass of the car is m sub two. The acceleration in the second case, a sub two, is represented by a shorter arrow than in the first case, a sub one.
Figure 2. The same force exerted on systems of different masses produces different accelerations. (a) A basketball player pushes on a basketball to make a pass. (The effect of gravity on the ball is ignored.) (b) The same player exerts an identical force on a stalled SUV and produces a far smaller acceleration (even if friction is negligible). (c) The free-body diagrams are identical, permitting direct comparison of the two situations. A series of patterns for the free-body diagram will emerge as you do more problems.
It has been found that the acceleration of an object depends only on the net external force and the mass of the object. Combining the two proportionalities just given yields Newton’s second law of motion.
NEWTON’S SECOND LAW OF MOTION
The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In equation form, Newton’s second law of motion is
a
=
F
net
m
a=Fnetm.
This is often written in the more familiar form
Fnet = ma.
When only the magnitude of force and acceleration are considered, this equation is simply
Fnet = ma.
Although these last two equations are really the same, the first gives more insight into what Newton’s second law means. The law is a cause and effect relationship among three quantities that is not simply based on their definitions. The validity of the second law is completely based on experimental verification.
Units of Force
Fnet = ma is used to define the units of force in terms of the three basic units for mass, length, and time. The SI unit of force is called the newton (abbreviated N) and is the force needed to accelerate a 1-kg system at the rate of 1 m/s2. That is, since Fnet = ma,
1 N = 1 kg ⋅ m/s2.
While almost the entire world uses the newton for the unit of force, in the United States the most familiar unit of force is the pound (lb), where 1 N = 0.225 lb.
Since Fnet and m are given, the acceleration can be calculated directly from Newton’s second law as stated in Fnet = ma.
Solution
The magnitude of the acceleration a is
a
=
F
net
m
a=Fnetm. Entering known values gives
a
=
51
N
24
kg
a=51 N24 kg
Substituting the units kg ⋅ m/s2 for N yields
a
=
51 kg
⋅
m/s
2
24 kg
=
2.1
m/s
2
a=51 kg⋅m/s224 kg=2.1 m/s2.
Discussion
Explanation:
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