# System of particles, linear momentum (easy problem)

• lemonpie
In summary, the task at hand involves a 2100 kg truck traveling north at 41 km/h, turning east and accelerating to 51 km/h. The change in the truck's kinetic energy is 74510 J. The magnitude and direction of the change in its momentum are 38178 kg m/s and 38.8 degrees, respectively. The solution involves vector operations and the final direction is South and East at 38 degrees.

## Homework Statement

A 2100 kg truck traveling north at 41 km/h turns east and accelerates to 51 km/h. (a) What is the change in the truck's kinetic energy? What are the (b) magnitude and (c) direction of the change in its momentum?

## Homework Equations

currently using delta P = mvf - mvi, but this is not working. i then tried p = mvcom, but this doesn't work either. please help.

## The Attempt at a Solution

first converted the speeds to 11.39 and 14.17 m/s.

a) delta K = 74510 J. this is correct.

b) Pi = (2100)(11.39) = 23919 kg m/s
Pf = (2100)(14.17) = 29757 kg m/s

delta P = Pf - Pi = 5838 kg m/s. this is incorrect.

c) i have no idea how to do this either.

Your problem with b) is that your momentum is changing in both x and y. Remember v and hence p are vectors.

wow, thanks so much! my new answer is 38178 kg m/s, which is correct.

any help with c) (from anyone) would be appreciated, but only if you have time and whatnot. thanks!

lemonpie said:
wow, thanks so much! my new answer is 38178 kg m/s, which is correct.

any help with c) (from anyone) would be appreciated, but only if you have time and whatnot. thanks!

c) is again a vector operation.

P_final - P_initial

Or more simply

P_final + (- P_initial)

In b) you found |ΔP|, now they want the angle right?

arctan(vy/vx) = 38.8 degrees um... i would have said northeast. but i guess that's not right (according to the back of the book). i mean, the magnitude of the angle is right. the direction isn't.

lemonpie said:
arctan(vy/vx) = 38.8 degrees um... i would have said northeast. but i guess that's not right (according to the back of the book). i mean, the magnitude of the angle is right. the direction isn't.

It was originally traveling north. Then it was going east. Hence it's "change" in direction north-south must be south and of course since it moved to the east then it is South and East at 38 degrees.

## 1. What is a system of particles in physics?

A system of particles in physics refers to a group of objects or bodies that are interacting with each other through forces or other physical interactions. These particles can be either stationary or in motion, and their behavior can be described using Newton's laws of motion.

## 2. What is linear momentum?

Linear momentum is a physical quantity that describes the amount of motion an object has in a straight line. It is defined as the product of an object's mass and its velocity and is a vector quantity with both magnitude and direction.

## 3. How is linear momentum conserved in a system of particles?

In a closed system, the total linear momentum remains constant, meaning it is conserved. This is known as the law of conservation of momentum. This means that the total momentum before and after a collision or interaction between particles will remain the same.

## 4. Can linear momentum be transferred from one particle to another?

Yes, linear momentum can be transferred from one particle to another through collisions or interactions between the particles. This transfer of momentum is what causes objects to move and change their velocity.

## 5. How is the momentum of a system of particles calculated?

The momentum of a system of particles can be calculated by adding together the individual momenta of each particle in the system. This can be represented mathematically as P = m1v1 + m2v2 + ... + mnvn, where P is the total momentum, m is mass, and v is velocity.