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alejandro alejandro
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7 years ago
Kathy and Bill collided at an intersection.  The police learned the mass of the truck is 3200 kg and the mass of the car is 2800 kg.  Based on the length of the skid marks at the scene and the mass of the vehicles, police estimate that the combined mass was moving at 7.0 m/s just after impact.  From this point, the two vehicles slid and came to rest at the corner of the intersection. 

Using the principle of conservation of momentum, the police determined that Bill’s truck was travelling at 2.3 m/s before the collision and Kathy’s car was travelling at 15 m/s before the collision.

The two momentum vectors before the collision are represented by the horizontal and vertical lines below.  The momentum after the collision is the slanted line.  Adding the two momentum vectors before the collision equals the momentum after the collision, according to the law of conservation of momentum

While the photo suggests a much more complex collision than the given diagram, assume that the diagram shows exactly what happened.

Using the vector diagram above and your calculated value for the momentum of the combined vehicles, verify the police’s calculations and determine the momentum and velocity of Bill’s truck just before the collision.

P.D:  I know the Magnitude of the momentum after the collision is 6000kg*7m/s=42000kg*m/s
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Hello everyone!

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wrote...
7 years ago
Yes, you have the right total magnitude of the momentum after an inelastic collision. However, that total magnitude applies only for the movement 80 degrees above x axis; however, the collision was in an INTERSECTION. Which creates a slight problem because there are two velocities and two momentum to be accounted for. Let's say the direction the truck is going is the x component and the direction the car was going is the y component.

So, for inelastic collision, m1v1+m2v2=(m1+m2)v3.

For the x component, the car was only moving in a y direction, so its initial velocity is zero in the x direction. The car's mass is 2800 kg. Truck, however, was moving in the x direction with a speed of vt with a mass of 3200 kg. The final x component momentum (note: only the x component) is the product of 6000 kg for the mass and 7*cos 80 m/s for the final x component velocity.

So, the equation is (2800)(0)+(3200)vt=(6000)(7*cos 80)

Solve for vt, and get 2.279132 and round to 2.3 m/s. The momentum is pretty self explanatory.

You could have also simply used the trigonometric functions with the total momentum. (42000)*(Cos 80)/3200. I just did it this way to illustrate the concept.
wrote...
A year ago
Thank you
wrote...
9 months ago
thank you
wrote...
2 weeks ago
The mass of the truck is 3200 kg, and the mass of the car is 2800 kg. Based on the length of the skid marks at the scene and the mass of the vehicles, police estimate that the combined mass was moving at 7.0 m/s just after impact. From this point, the two vehicles slid and came to rest at the corner of the intersection.
•   Determine the magnitude of the momentum just after the collision.

•   Is this the same as the magnitude of the momentum just before the collision? Explain why or why not.
wrote...
Educator
2 weeks ago
The mass of the truck is 3200 kg, and the mass of the car is 2800 kg. Based on the length of the skid marks at the scene and the mass of the vehicles, police estimate that the combined mass was moving at 7.0 m/s just after impact. From this point, the two vehicles slid and came to rest at the corner of the intersection. • Determine the magnitude of the momentum just after the collision. • Is this the same as the magnitude of the momentum just before the collision? Explain why or why not.

Here's the answer:
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wrote...
2 weeks ago
You have already determined the magnitude of the momentum of the combined vehicles just after impact and the kinetic energy before and after the impact. The following vector diagram illustrates the direction of the momentum vector based on evidence from the scene.
The two momentum vectors before the collisions are represented in blue. The momentum after the collision is in red. Adding the two momentum vectors before the collision equals the momentum after the collision, according to the law of conservation of momentum.
 
While the opening photo suggests a much more complex collision than the given diagram, assume that the diagram shows exactly what happened.
•   Using this vector diagram and your calculated value for the momentum of the combined vehicles, verify the police calculations and determine the momentum and velocity of Bill’s truck just before the collision.
•   Using this vector diagram and your calculated value for the momentum of the combined vehicles, verify the police calculations and determine the momentum and velocity of Kathy’s car just before the collision.
•   Does your analysis prove, beyond a reasonable doubt, that Kathy was, in fact, travelling at the speed limit of 50 km/h just prior to the accident? What assumptions did you make in your solution to determine this?
wrote...
Educator
2 weeks ago
Please start a new topic for a new question
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