# Change in Momentum using Vectors

In summary, the magnitude of change in momentum of an object in the xy plane can be found by integrating the force over the time interval of interest. In this case, the force F = (2ti + 3t^2j) N results in a change in momentum of 4i + 8j.

## Homework Statement

A force F = (2ti + 3t^2j) N acts on an object moving in the xy plane. Find the magnitude of change in momentum of the object in time interval t=0 to t=2
(The bold ones are vectors)

## Homework Equations

Ft=change in momentum

## The Attempt at a Solution

magnitude of F = (4t^2 + 9t^4)^(1/2)
taking t^2 common:
t(4+9t^2)^(1/2)
Ft=delta p
so, delta p = 2t(4 + 9t^2 ) ^ (1/2)

But the answer doesn't have ts in it.

Have you learned calculus? The force is time-dependent, so you will have to perform an integration to find out the total change in momentum over the time interval.

Fightfish said:
Have you learned calculus? The force is time-dependent, so you will have to perform an integration to find out the total change in momentum over the time interval.
I have learned it. But have never actually used it in physics.
So I integrate F?
Like:
Integration of 2ti+3t^2 j
is t^2i + t^3j
with the limits 0 and 2
Then,
4i + 8j is the change in p

Yes. You can understand the integration process by looking at Newton's second law, which states that $$\vec{F} = \frac{d\vec{p}}{dt}$$, and so this immediately results in $$\Delta p = \int_{t_0}^{t_f}\vec{F} dt$$

Fightfish said:
Yes. You can understand the integration process by looking at Newton's second law, which states that $$\vec{F} = \frac{d\vec{p}}{dt}$$, and so this immediately results in $$\Delta p = \int_{t_0}^{t_f}\vec{F} dt$$
Thank you!

## 1. What is momentum and how is it calculated?

Momentum is a physics concept that refers to the quantity of motion an object has. It is calculated by multiplying an object's mass by its velocity.

## 2. What is change in momentum?

Change in momentum refers to the difference in an object's momentum between two points in time. It can be calculated by subtracting the initial momentum from the final momentum.

## 3. How do vectors play a role in calculating change in momentum?

Vectors play a critical role in calculating change in momentum because they represent both the magnitude and direction of an object's velocity. Since momentum is a vector quantity, it must take into account the direction of an object's motion.

## 4. What is the equation for change in momentum using vectors?

The equation for change in momentum using vectors is ∆p = m∆v, where ∆p is the change in momentum, m is the mass of the object, and ∆v is the change in velocity.

## 5. How can understanding change in momentum using vectors be applied in real-world situations?

Understanding change in momentum using vectors is essential in fields such as engineering, physics, and sports. In engineering, it is used to design safer car crashes and prevent damage to structures during earthquakes. In physics, it helps to explain the motion of objects in collisions and explosions. In sports, it is crucial in analyzing the performance of athletes, such as the impact of a baseball bat on a ball or the speed of a hockey puck after being hit by a stick.

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