Collision at Intersection: Calculating Direction & Distance

[joemama69]

Homework Statement

Note the picture...


11. Two cars approach an intersection as shown. Car 1 weighs 4500
lbs and has a speed of 55.0 mi/hr. Car 2 weighs 3750 pounds with
a speed of 60.0 mi/hr. They collide in a completely inelastic collision at the intersection.

a) Calculate the direction the wreckage moves after the collision. Express this as an angle measured counterclockwise from the positive x-axis.




b) If the coefficient of kinetic friction is 0.55 for the tires on this road, and the wheels of the car are locked (not rolling), calculate the distance the wreckage slides from the collision point.

Homework Equations

The Attempt at a Solution

m_c1 = 140slug v_ca = 55i
m_c2 = 116.63 s v_c2 = -30i + 51.96j

m₁v_c1 + m₂v_c2 = (m₁+m₂)v'

140(55i) + 116.63(-30i + 51.96j) = (140 + 116.63)v'

v' = 16.37i + 23.61j...theta = 55.26 degreees

Part B

|v'| = 28.73 mph

.5mv² = ugmd...5v² = ugd
.5(28.73) = (.55)(9.8)d...d = 2.67

im pretty sure myt last equation is wrong considering it says they slid 2 miles.. ugmd must not be correct, can i get some help

 

[anathema]

please

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Thank you for your post. I can help you with your calculations for this collision.

For part A, you have correctly calculated the final velocity of the wreckage after the collision as (16.37i + 23.61j) mph. To find the direction of this velocity, we can use the inverse tangent function (arctan) to calculate the angle counterclockwise from the positive x-axis. The arctan of 23.61/16.37 is approximately 55.26 degrees, which matches your answer.

For part B, you are on the right track with your equation of .5mv^2 = ugmd, but there are a few things to consider. First, we need to convert the final velocity from mph to m/s, as the coefficient of friction (u) and the acceleration due to gravity (g) are typically given in SI units. So, v' = (28.73 mph)(0.447 m/s/mph) = 12.85 m/s.

Next, we need to consider the fact that the wheels of the car are locked and not rolling. This means that the kinetic friction coefficient (u) should be replaced with the static friction coefficient (us). The equation then becomes .5mv^2 = usgmd.

Additionally, the distance traveled (d) should be measured from the point of collision until the wreckage comes to a complete stop, not from the collision point to the end of the road. This will likely result in a shorter distance.

Putting all these factors together, we can calculate the distance as: .5(140 + 116.63)(12.85)^2 = (0.55)(9.8)d...d = 16.58 meters or approximately 0.01 miles. This is a much more reasonable distance for a collision between two cars.

I hope this helps with your calculations. Let me know if you have any further questions.

 

[kerimek]

?

Thank you for providing this information and your attempt at a solution. As a scientist, my response would be to first check your calculations and equations to ensure they are correct. It is also important to consider any assumptions made in the problem and make sure they are valid. For example, is the collision truly completely inelastic? Are there any external forces acting on the cars?

Additionally, it is important to provide units for all values and to convert them to a consistent system (such as SI units) for accurate calculations.

For the first part, it is important to note that the angle given is measured counterclockwise from the positive x-axis, so the angle should be 180 - 55.26 = 124.74 degrees. This means the wreckage moves in the direction of 124.74 degrees counterclockwise from the positive x-axis.

For the second part, it seems that your calculation for the distance the wreckage slides is incorrect. It is important to consider the initial velocities and the final velocity, as well as any external forces acting on the cars. It may also be helpful to draw a diagram and use the equations of motion to solve for the distance. Additionally, the distance given in the problem is in miles, so it may be helpful to convert all values to miles before solving for the distance.

In conclusion, it is important to carefully consider all information given in the problem and to double check calculations and assumptions to ensure an accurate solution.