# Expression for the force on a particle

• Nightrider55
In summary, the problem is asking for the force exerted on a particle at a given time, given its momentum at that time. This can be found using Newton's second law, which states that force equals the rate of change of momentum. Therefore, the expression for Fx(t) is 12t kg m/s^2. This may seem like a simple problem, but it can be more difficult if not familiar with calculus and the general form of Newton's law.
Nightrider55

## Homework Statement

A particle of mass m is at rest at t=0. Its momentum for t>0 is given by Px=6t^2 kg m/s, where t is in s. Find an expression for Fx(t), the force exerted on the particle as a function of time.

Px=MVx

## The Attempt at a Solution

The question seems really simple but momentum confuses me. I know that momentum is related to the area under the Fx(t)curve between Ti and Tf by Pfx-Pix or the change in momentum, but I don't know where to go from there. Something to get me headed in the right direction would be greatly appreciated!

Hint: Newton's second law states that:

$$\vec{F} = \frac{d \vec{p}}{dt}$$

so then it would be F=12t. That seems a little too easy. When they say Px would I also have to find Py in order to find the mag of P?

Nightrider55 said:
so then it would be F=12t. That seems a little too easy.

Maybe it is. What level of physics are you taking? Is it calculus-based? It's clear that you already know how to differentiate. If your prof expected you to be familar with calculus and to be aware that F = dp/dt was the true (most general) form of Newton's law, then yes, he has assigned a trivial problem. However, if you prof did not expect you to be familiar with calculus or F = dp/dt, then maybe he thought he had given you a stumper.

By the way, WERE you aware that F = dp/dt before I told you? If not, can you see that F = ma follows from this relation provided the mass of the particle is constant?

Nightrider55 said:
When they say Px would I also have to find Py in order to find the mag of P?

No. Why would you? They don't ask you for P or Py. They only ask for Px.

cepheid said:
Maybe it is. What level of physics are you taking? Is it calculus-based? It's clear that you already know how to differentiate. If your prof expected you to be familar with calculus and to be aware that F = dp/dt was the true (most general) form of Newton's law, then yes, he has assigned a trivial problem. However, if you prof did not expect you to be familiar with calculus or F = dp/dt, then maybe he thought he had given you a stumper.

By the way, WERE you aware that F = dp/dt before I told you? If not, can you see that F = ma follows from this relation provided the mass of the particle is constant?

No. Why would you? They don't ask you for P or Py. They only ask for Px.

I am in calculus physics and I talked to my teacher and he didn't realize that he assigned such an easy problem :rofl:

I was aware that F = dp/dt before you told me but I didn't use it because I thought I was missing something because it seemed too simple of a problem considering it was among the more difficult problems at the end of the chapter.

## 1. What is the expression for the force on a particle?

The expression for the force on a particle is F = ma, where F is the force, m is the mass of the particle, and a is the acceleration.

## 2. How is the expression for the force on a particle derived?

The expression for the force on a particle is derived from Newton's Second Law of Motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

## 3. Can the expression for the force on a particle be used for all types of forces?

Yes, the expression for the force on a particle can be used for all types of forces, including gravitational, electromagnetic, and frictional forces.

## 4. What are the units of the expression for the force on a particle?

The units of the expression for the force on a particle are Newtons (N), which is equivalent to kg*m/s^2.

## 5. How is the expression for the force on a particle used in real-world applications?

The expression for the force on a particle is used in a variety of real-world applications, such as calculating the forces acting on a rocket during launch, determining the impact of a collision between two objects, and analyzing the motion of objects in a gravitational field.

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