# Momentum Problem on a particle

• Nightrider55
In summary, the homework statement states that if a 420 g particle is subjected to a force of 10 N for a time interval of less than or equal to 2 seconds, the particle's speed at t=2 seconds will be 2.19 m/s.
Nightrider55

## Homework Statement

Force F_x =(10N){sin({(2pi(t))/4.0s) (where t in (m/s) is exerted on a 420 g particle during the interval 0 less than or equal to T is less than or equal to 2 seconds.

If the particle starts at rest what is its speed at t=2 seconds?

## Homework Equations

Jx= area under the Fx(t) cureve between Ti and Tf

Pfi-Pix=Jx

## The Attempt at a Solution

This problem looks fairly easy but I am having trouble setting it up. I took the integral of the force over the time interval and got .54817 Ns which should be the impulse. I then used this to find Pfx by the equation above. I then used Vfx=(Pfx/m) to find the final velocity which came out to be 2.19 m/s but its wrong, any insight as to what I did wrong?

integral of F(t)= impulse= change of momentum= Final momentum, since intial velocity is zero.
Final momentum divide by the mass, .420kg, would equal the velocity.

I do not have a calculator right now but I am sure this is it :)

oh by the way, when integrating force, you might want to include absolute value around F(t)

Last edited:
It keeps on saying my answer is wrong. What am I missing?

Use this:
$$F=m\frac{dv}{dt}$$

You know integration, right ?

Yea I think I am doing it right, after I integrate it I get 12.73 then you say times that by the mass, so 12.73 x .42kg= 5.35. That should be right, could someone double check.

I integrated Fdt from t=0 to t=2 and got (40/pi)*N*sec. Why are you getting .54817Ns? Can you show details?

I got this on integrating:
$$0.042v=-\frac{2}{\pi}cos(\frac{\pi t}{2})+\frac{2}{\pi}$$

for t=2 it gives v=30.33 m/s.

Ok, impulse=40/pi*Ns=12.73*Ns=m*v. That's good. Don't you want to divide the impulse by the mass to get velocity?

Last edited:

## 1. What is momentum?

Momentum is a measure of an object's motion, and is defined as the product of its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is momentum calculated?

Momentum is calculated by multiplying an object's mass (m) by its velocity (v). The formula for momentum is p = m * v.

## 3. What is the unit of momentum?

The unit of momentum is kilogram-meter per second (kg*m/s) in the SI system of units. In other systems, it may be expressed in units of gram-centimeter per second (g*cm/s) or pound-foot per second (lb*ft/s).

## 4. What is the relationship between force and momentum?

According to Newton's Second Law of Motion, force is equal to the rate of change of an object's momentum. In other words, the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a).

## 5. How is momentum conserved in a closed system?

In a closed system, the total momentum remains constant, meaning it is conserved. This is known as the law of conservation of momentum. This means that the total momentum before an interaction or collision is equal to the total momentum after the interaction or collision.

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