2D - Momentum Question, Grade 12 Canadian Physics

In summary, two cars with masses of 1,400kg and 1,300kg collide at an intersection with velocities of 45 km/h[S] and 39 km/h[E] respectively. The cars experience an inelastic collision and their velocities after the collision are 30 km/h [51 South of East]. The conservation of momentum equation, P total = P total prime, is used to solve for the final velocity. The correct answer is achieved by considering the total momentum, rather than the total velocity, of the system and using a vector diagram to calculate the required theta value.
  • #1

Homework Statement


2 cars collide at an intersection.
one car which has a mass of 1,400kg has a velocity of 45 km/h;
the other car has a mass of 1,300kg and has a velocity of 39 km/h[E]
The cars has an inelastic collision. What are their velocity after the collision


Homework Equations



Conservation of momentum: P total = P total prime


The Attempt at a Solution



I have tried on numerous occasions but have not achieved the correct answer.

The correct answer should be: "30 km/h [ 51 South of East.]

I got the correct magnitude of the velocity which is 30 km/h. Easy enough, but i didn't get the degrees required. Additional vector diagram is appreciated.
 
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  • #2
Try to draw the vector diagram for the initial total momentum of the system.
 
  • #3
@grzz I figured out what i did wrong. When i calculated for the theta of the vector triangle. I simply used the velocities. Instead i tried it with m(v) and it worked for me. Thanks.
 
  • #4
You just confirmed that it is the total momentum that is conserved and not the total velocity!
 
  • #5



I would approach this problem by first setting up a coordinate system, with the x-axis pointing east and the y-axis pointing north. I would then use the conservation of momentum equation, P total = P total prime, to solve for the final velocities of the two cars.

Let us assume that the car with a mass of 1,400kg is traveling in the positive x-direction (east) and the car with a mass of 1,300kg is traveling in the positive y-direction (north).

Using the given information, we can calculate the initial momentum of each car as follows:

P1 = m1v1 = (1,400kg)(45 km/h) = 63,000 kg*km/h [E]
P2 = m2v2 = (1,300kg)(39 km/h) = 50,700 kg*km/h [N]

Since this is an inelastic collision, the two cars will stick together after the collision and move in the same direction. Therefore, the final momentum of the combined cars will be:

P total prime = (m1 + m2)v final

Using the conservation of momentum equation, we can equate the initial momentum to the final momentum and solve for the final velocity:

P total = P total prime
63,000 kg*km/h [E] + 50,700 kg*km/h [N] = (1,400kg + 1,300kg)v final
113,700 kg*km/h [E] = 2,700kg v final

Dividing both sides by 2,700kg, we get:

v final = 42 km/h [E]

Therefore, the final velocity of the combined cars after the collision will be 42 km/h [E].

To find the direction of the final velocity, we can use the tangent function:

tan θ = (v final y)/(v final x)
tan θ = (42 km/h)/(42 km/h)
θ = tan^-1(1)
θ = 45°

Since the final velocity is in the east direction (positive x-axis), the angle of 45° indicates that the final velocity is moving 45° south of east.

Therefore, the final velocity of the combined cars after the collision is 42 km/h [45° South of East].
 

1. What is momentum in 2D physics?

Momentum is a physical quantity that describes the motion of an object in 2D space. It is defined as the product of an object's mass and velocity in a particular direction.

2. How is momentum calculated in 2D physics?

Momentum in 2D physics is calculated by multiplying an object's mass by its velocity in the x-direction and in the y-direction separately. The total momentum can then be found by using the Pythagorean theorem to calculate the magnitude of the momentum vector.

3. How does the conservation of momentum apply in 2D collisions?

The conservation of momentum states that the total momentum of a system remains constant before and after a collision. In 2D collisions, this means that the total momentum in the x-direction and in the y-direction must remain constant separately.

4. How is the momentum principle applied in 2D physics?

The momentum principle states that the net force acting on an object is equal to the rate of change of its momentum. In 2D physics, this means that the net force in the x-direction and in the y-direction must be considered separately.

5. How does momentum affect the motion of objects in 2D space?

Momentum plays a crucial role in determining the motion of objects in 2D space. The direction of an object's momentum determines the direction in which it will continue to move, while the magnitude of its momentum determines its speed. In collisions, the transfer of momentum between objects can result in changes in their individual velocities.

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