Solving an Inelastic Collision: Finding the Angle of Motion for Two Cars

In summary, two cars, a red car with a mass of 1000kg traveling at 15m/s and a blue car with a mass of 1500 kg traveling at 20m/s, collide at an intersection and stick together. Using the conservation of momentum, the velocity of the combined cars is found to be approximately 13.5 m/s at an angle of 27 degrees north of east. This is determined by using the equations Vf = √(Vfx2) + (Vfy2), m1vf1x+ m2vf2x= m1vi1x + m2vix for the x component, and m1vf1y+ m2vf2y= m1
  • #1
alexito01
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0

Homework Statement



A red car and a blue car collide at an in intersection. Prior to the collision the red car with mass 1000kg was heading North at 15m/s. The blue car with mass 1500 kg was heading East at 20m/s. The collision is completely inelastic with the cars sticking together and moving as one. At what angle measured North of East do the cars move off?

Homework Equations


I used Vf = √(Vfx2) + (Vfy2)

I alsoUsed m1vf1x+ m2vf2x= m1vi1x + m2vix for x component and
m1vf1y+ m2vf2y= m1vi1y + m2viy for y component

and then θ = tan-1(vfy/vfx) to findthe angle but i keep geting it wrong

The Attempt at a Solution


I ended up with an angle of around 27 degrees
 
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  • #2
This is a conservation of momentum problem, not conservation of energy as your title suggests. However, your method looks good and I agree with your answer. What's wrong with it?
 
  • #3
That is correct about 27 degrees north of east. at a velocity about 13.5 m/s (13 with 2 sig figs)
 
  • #4
Cars stick after collision. So they have common velocity. Let velocity = vf
Take east as +ve x and north as +ve y

For x component:-
(m1+m2)vfx = m1vi1x + m2vix
(1000+1500)vfx = 1000*0 + 1500*20
2500 vfx = 30000
vfx = 30000/2500 = 300/25
vfx = 12 m/s

For y component
(m1+m2)vfy = m1vi1y + m2viy
(1000+1500)vfy = 1000*15 + 1500*0
2500 * vfy = 15000
vfy = 15000/2500 = 150/25 = 6 m/s

theta = tan-1(vfy/vfx) = tan-1(6/12) = tan-1(1/2) = 26.565 deg
So, as approximation, this is same as your answer. Why do you think your answer is wrong?
 

FAQ: Solving an Inelastic Collision: Finding the Angle of Motion for Two Cars

What is conservation of energy?

Conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, but can only be transformed from one form to another.

Why is conservation of energy important?

Conservation of energy is important because it helps us understand and predict the behavior of physical systems. It also allows us to develop efficient and sustainable energy sources.

How does conservation of energy apply to everyday life?

Conservation of energy applies to everyday life in many ways, such as in the use of renewable energy sources, the design of energy-efficient buildings and appliances, and the concept of energy conservation in personal habits and behaviors.

What are some real-life examples of conservation of energy?

Some real-life examples of conservation of energy include a pendulum swinging back and forth, a rollercoaster moving up and down, and a light bulb converting electrical energy into light and heat.

What are the consequences of not following the principles of conservation of energy?

If the principles of conservation of energy are not followed, it can lead to energy waste and inefficiency, as well as potential environmental consequences such as increased greenhouse gas emissions and depletion of natural resources.

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