# Momentum: Glancing collisions in two dimensions

• anti404
In summary, the conversation discusses a problem involving a collision between two balls, one with a mass of 2kg and a velocity of 6m/s traveling North, and the other identical and stationary. After the collision, one ball moves with a velocity of 2m/s at an angle of 30 degrees East of North, and the goal is to find the velocity of the other ball. Through conservation of momentum and using equations for x and y components, the conversation leads to solving for the angle theta and finding the velocity of the second ball by substituting values and using trigonometric functions.
anti404

## Homework Statement

a ball of mass 2kg is traveling North with a Velocity 6m/s when it collides with an identical, stationary ball. after the collision, one of the ball moves with a velocity of 2m/s at an angle of 30deg east of north. find Velocity of the other ball.
m1=2kg
m2=m1
v1=6m/s
v1'=2m/s
alpha=30deg
v2'=?
theta=?

## Homework Equations

P(initial)=P(final) <--conservation of momentum
P=mv

## The Attempt at a Solution

split the (conserved) momentum into x and y components.
Px: 0+0=m1v1'sin(alpha)-m1v2'sin(theta)
Py: m1v1=m1v1'cos(alpha)+m1v2'cos(theta)

after that, I'm lost. I honestly have no idea where to go from there. I think maybe you're supposed to solve for... theta? and then plug that in. but again, I don't know how to do so. we just barely[and when I mean barely, I mean for about 1 minute at the end of class] covered this today, and our book details only inelastic collisions in two dimensions, which is of little help here, as it is not stated to be elastic or inelastic. help would be very, VERY much appreciated.

Px: 0+0=m1v1'sin(alpha)-m1v2'sin(theta)
Py: m1v1=m1v1'cos(alpha)+m1v2'cos(theta)

Rewrite these equations as
m1v1'sin(alpha) = m1v2'sin(theta)...(1)
m1v1- m1v1'cos(alpha) = m1v2'cos(theta)...(2)
Cancel m1 form both sides.Substitute the values of v1' and α.
Find v2' from eq.(1) and substitute in eq.(2) and solve for θ.

remember that, like in a snooker game, these balls paths after the collision will be 90 degrees apart.

rl.bhat said:
Px: 0+0=m1v1'sin(alpha)-m1v2'sin(theta)
Py: m1v1=m1v1'cos(alpha)+m1v2'cos(theta)

Rewrite these equations as
m1v1'sin(alpha) = m1v2'sin(theta)...(1)
m1v1- m1v1'cos(alpha) = m1v2'cos(theta)...(2)
Cancel m1 form both sides.Substitute the values of v1' and α.
Find v2' from eq.(1) and substitute in eq.(2) and solve for θ.

this is what I kept trying to do, but I don't know how to solve for v2' since you're missing angle theta. because what I'd get was m1v1'sin(alpha)/sin(theta)=v2'. and I don't know how to solve from that point on.

Lachlan1: would that mean that you'd just add 90deg to alpha and you'd get theta...?

v1'sin(alpha) = v2'sin(theta)...(1)
v1- v1'cos(alpha) = v2'cos(theta). (2)
From eq.(1) and (2) you will get
v1'sin(alpha)/[v1- v1'cos(alpha)/ = v2'sin(theta)/v2'cos(theta)...
Substitute the values of v1. v1' and α. Simplify and find tanθ. From that find θ.

rl.bhat said:
v1'sin(alpha) = v2'sin(theta)...(1)
v1- v1'cos(alpha) = v2'cos(theta). (2)
From eq.(1) and (2) you will get
v1'sin(alpha)/[v1- v1'cos(alpha)/ = v2'sin(theta)/v2'cos(theta)...
Substitute the values of v1. v1' and α. Simplify and find tanθ. From that find θ.

ah, okay. for whatever reason I kept getting cos/sin, which confused me. thanks!

## 1. What is momentum?

Momentum is a measurement of an object's motion and is calculated by multiplying its mass by its velocity. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is momentum conserved in glancing collisions?

In a glancing collision, momentum is conserved because the total momentum of the objects before the collision is equal to the total momentum after the collision. This means that the total mass and velocity of the objects do not change.

## 3. What is the difference between elastic and inelastic collisions?

In an elastic collision, both momentum and kinetic energy are conserved, meaning that the objects bounce off each other without any loss of energy. In an inelastic collision, some of the kinetic energy is converted to other forms of energy, such as heat or sound.

## 4. How do you calculate the momentum of an object?

The momentum of an object is calculated by multiplying its mass (in kilograms) by its velocity (in meters per second). The formula for momentum is p = mv.

## 5. Why is momentum an important concept in physics?

Momentum is an important concept in physics because it helps us understand the motion of objects and how they interact with each other. It is also a conserved quantity, meaning it remains constant in a closed system, making it a valuable tool in solving complex physics problems.

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