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Oct 1, 2024 · There are a few ways of stating Newton’s second law of motion: Force (F) equals the rate of change of momentum of an object (dp) with respect to time (dt). F = dp / dt. Force (F) equal mass (m) multiplied by acceleration (a). This works when mass remains constant, as in classical mechanics. F = m·a.
The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system and is inversely proportion to its mass. In equation form, Newton’s second law is. a = F net m, (5.4.3) where a is the acceleration, F net is the net force, and m is the mass.
Newton's second law, or fundamental principle of dynamics, states that a resultant force exerted on an object is always equal to the product of the object's mass and its acceleration. Furthermore, the acceleration produced and the resultant force have the same orientation.
- Overview
- What is Newton's second Law?
- What does net force mean?
- How do we use Newton's second law?
- What do we do when a force is directed at an angle?
- Example 1: Newton the turtle
- Example 2: String cheese
Review your understanding of Newton's second law in this free article aligned to NGSS standards.
What is Newton's second Law?
In the world of introductory physics, Newton's second law is one of the most important laws you'll learn. It's used in almost every chapter of every physics textbook, so it's important to master this law as soon as possible.
We know objects can only accelerate if there are forces on the object. Newton's second law tells us exactly how much an object will accelerate for a given net force.
a=ΣFm
To be clear, a is the acceleration of the object, ΣF is the net force on the object, and m is the mass of the object.
In the world of introductory physics, Newton's second law is one of the most important laws you'll learn. It's used in almost every chapter of every physics textbook, so it's important to master this law as soon as possible.
We know objects can only accelerate if there are forces on the object. Newton's second law tells us exactly how much an object will accelerate for a given net force.
a=ΣFm
To be clear, a is the acceleration of the object, ΣF is the net force on the object, and m is the mass of the object.
[Wait, I thought Newton's second law was F=ma?]
Looking at the form of Newton's second law shown above, we see that the acceleration is proportional to the net force, ΣF , and is inversely proportional to the mass, m . In other words, if the net force were doubled, the acceleration of the object would be twice as large. Similarly, if the mass of the object were doubled, its acceleration would be half as large.
A force is a push or a pull, and the net force ΣF is the total force—or sum of the forces—exerted on an object. Adding vectors is a little different from adding regular numbers. When adding vectors, we must take their direction into account. The net force is the vector sum of all the forces exerted on an object.
[What does the term vector sum mean?]
For instance, consider the two forces of magnitude 30 N and 20 N that are exerted to the right and left respectively on the sheep shown above. If we assume rightward is the positive direction, the net force on the sheep can be found by
ΣF=30 N−20 N
ΣF=10 N to the right
If there were more horizontal forces, we could find the net force by adding up all the forces to the right and subtracting all the forces to the left.
If the problem you're analyzing has many forces in many directions, it's often easier to analyze each direction independently.
In other words, for the horizontal direction we can write
ax=ΣFxm
This shows that the acceleration ax in the horizontal direction is equal to the net force in the horizontal direction, ΣFx , divided by the mass.
Similarly, for the vertical direction we can write
ay=ΣFym
When forces are directed in diagonal directions, we can still analyze the forces in each direction independently. But, diagonal forces will contribute to the acceleration in both the vertical and horizontal directions.
For instance, let's say the force F3 on the hen is now directed at an angle θ as seen below.
The force F3 will affect both the horizontal and vertical accelerations, but only the horizontal component of F3 will affect horizontal acceleration; only the vertical component of F3 will affect the vertical acceleration. So we'll break the force F3 into horizontal and vertical components as seen below.
Now we see that the force F3 can be viewed as consisting of a horizontal force F3x and a vertical force F3y .
Using trigonometry, we can find the magnitude of the horizontal component with F3x=F3cosθ . Similarly, we can find the magnitude of the vertical component with F3y=F3sinθ .
[Wait, how did we find this?]
A 1.2 kg turtle named Newton has four forces exerted on it as shown in the diagram below.
What is the horizontal acceleration of Newton the turtle?
What is the vertical acceleration of Newton the turtle?
To find the horizontal acceleration we'll use Newton's second law for the horizontal direction.
ax=ΣFxm(Start with Newton’s 2nd law for the horizontal direction.)
ax=(30 N)cos30∘−22 N1.2 kg(Plug in horizontal forces with correct negative signs.)
A wedge of cheese is suspended at rest by two strings which exert forces of magnitude F1 and F2 , as seen below. There is also a downward force of gravity on the cheese of magnitude 20 N .
What is the magnitude of the force F1 ?
What is the magnitude of the force F2 ?
We'll start by either using the horizontal or vertical version of Newton's second law. We don't know the value of any of the horizontal forces, but we do know the magnitude of one of the vertical forces—20 N . Since we know more information about the vertical direction, we'll analyze that direction first.
ay=ΣFym(Start with Newton’s 2nd law for the vertical direction.)
ay=F1sin60∘−20 Nm(Plug in vertical forces with correct negative signs.)
Newton's Second Law as a Guide to Thinking The numerical information in the table above demonstrates some important qualitative relationships between force, mass, and acceleration. Comparing the values in rows 1 and 2, it can be seen that a doubling of the net force results in a doubling of the acceleration (if mass is held constant).
Oct 21, 2024 · 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 = Fnet m. This is often written in the more familiar form.
People also ask
How does newton's second law work?
What is newton's second law of motion?
How does newton's second law explain the behavior of objects?
What is newton's second law in equation form?
How is newton's second law related to his first law?
What does newton's second law of motion tell us about nature?
In equation form, Newton’s second law of motion is a = Fnet m. This is often written in the more familiar form: Fnet = ma. The weight w of an object is defined as the force of gravity acting on an object of mass m. The object experiences an acceleration due to gravity g: w = mg.
