# Question about Newton's first law

• coconut62
In summary, C is the incorrect answer because the total energy of the body does not stay the same when external forces are cancelled out.
coconut62

## Homework Statement

Q13
All external forces on a body cancel out.
Which statement must be correct?

A The body does not move.
B The momentum of the body remains unchanged.
C The speed of the body remains unchanged.
D The total energy of the body remains unchanged.

## The Attempt at a Solution

I know that B is the best answer and that A and D is wrong, but I don't know why C is incorrect.

If you cancel out every forces on the body, surely the body will continue its motion with the same velocity in a straight line, and since the direction of motion is constant, then certainly the speed should be the same too.

Now consider a circular object being applied a torque. My question is, since the lines of action do not meet, can you say that the forces "cancel out"?

If you say that it does cancel out, then considering the changing of the velocity of the circular object, B would be wrong.

If you say it doesn't cancel out, that means torques/moments are not considered in this question at all, so what is left is just bodies traveling in a straight line whose speed can't possibly change when there's no external force. So does this support my claim that C is correct?

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C is the most correct in my opinion.

No - B is the best answer because

Force is defined as the net rate of change of momentum.[STRIKE][/STRIKE]

$$\sum_i \vec{F_i}=0 = \frac{d \vec{\ p}}{dt}$$

However, the momentum being constant does not mean that the speed has to be the same, nor the Energy to be the same.

Mathematically you can see it like:

$$\frac{ d\vec{p} }{dt } = 0 = m \frac{d \vec{v}} {dt} + \vec{v} \frac{d m }{dt }$$
$$\frac{d \vec v}{dt} = \frac{-1}{m} \left(\vec{v} \underbrace{\frac{d m}{dt}}_{\neq 0}\right)$$

This is a tricky point, however, physically you can think about it like this:

If the moving object (say at a constant velocity) loses some its mass while traveling (or the "effective" mass of the object is changing for some reason) the velocity could increase while the momentum is constant (due to decreasing mass),

Similarly, you can express Kinetic Energy as:

$$E = \frac{|\vec{p}^2|}{2 m}$$ and even if the momentum is constant, a change in mass could change the total Energy ..., hence D isn't the correct answer either.Hope this helps,
sokrates.

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1 person

## 1. What is Newton's first law?

Newton's first law, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force.

## 2. Who is Newton and why is his first law important?

Sir Isaac Newton was an English physicist and mathematician who is widely recognized as one of the most influential scientists in history. His first law is important because it laid the foundation for understanding the behavior of objects in motion and is a fundamental principle of classical mechanics.

## 3. How does Newton's first law apply to everyday life?

Newton's first law can be observed in many everyday situations. For example, when a car comes to a stop, the passengers inside will continue moving forward until they are stopped by the seat belt or airbag. This is because of inertia, the tendency of an object to resist changes in its state of motion.

## 4. What is the difference between Newton's first law and the law of conservation of momentum?

While Newton's first law describes the behavior of individual objects, the law of conservation of momentum is a broader law that applies to systems of objects. It states that the total momentum of a closed system remains constant, unless acted upon by an external force.

## 5. Can Newton's first law be violated?

In theory, Newton's first law cannot be violated. However, in certain extreme conditions such as in outer space or at the subatomic level, the effects of other forces may become more significant and the law may appear to be violated. Additionally, objects on Earth may appear to violate the first law due to the presence of friction and other external forces.

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