A 6000-kg truck traveling north at 5.0 m/s collides with a 4000-kg truck moving west at 15 m/s. If the two trucks remain locked together after impact, with what speed and in what direction do they move immediately after the collision?
The final speed and direction of locked trucks after collision, given that the truck of mass
Answer to Problem 44SP
Solution: The speed of the locked trucks is
Explanation of Solution
Given data:
The mass of the truck travelling north is
The speed of the truck travelling north is
The mass of the truck travelling west is
The speed of the truck travelling west is
Formula used:
The momentum of a body is expressed as,
Here,
Understand that during a collision between bodies 1 and 2, when the bodies after the collision combine to form a single body, the momentum in a particular direction before and after the collision is expressed as,
Here,
The resultant of the horizontal and vertical components of velocity is expressed as,
Here,
The direction of inclination of the resultant velocity with the horizontal is expressed as,
Here,
Explanation:
Consider the truck moving north as body A and the truck moving west as body B. Also, assuming positive x-direction as East direction and positive y-direction as North direction.
Now, consider the expression for initial momentum of body A in x-direction before collision
Here,
Understand that body A or the truck of mass
Consider the expression for initial momentum of body B in x-direction before collision
Here,
Understand that the body B or the truck of mass
Understand that according to the problem, after the collision, both the bodies form a single system and move as a single body having mass equal to sum of masses of body A and body B.
Consider the mass of the final combined body after the collision
Here,
Substitute
Consider the expression for the momentum of the combined system after collision
Here,
Substitute
Consider the expression for conservation of momentum for the collision
Substitute
The negative sign indicates that the horizontal component of velocity is in the negative x-direction that is towards west. Therefore, the velocity of the combined system in x-direction is
Consider the expression for initial momentum of body A in y-direction before collision
Here,
Understand that body A or the truck of mass
Consider the expression for initial momentum of body B in y-direction before collision
Here,
Understand that body B or the truck of mass
Consider the expression for the momentum of the combined system after collision
Here,
Substitute
Consider the expression for conservation of momentum for the collision.
Substitute
The positive sign indicates that the vertical component of velocity is in the positive y-direction that is toward north. Therefore, the component of velocity of the combined system in y-direction is
Write the expression for resultant final velocity of the system.
Substitute
The velocity of locked trucks is
Consider the expression for angle made by the resultant velocity with the horizontal.
Here,
Substitute
The negative sign indicates that the angle is measured in clockwise direction from the x-axis. Therefore, the resultant velocity is inclined at an angle
Conclusion:
The speed of the locked trucks is
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Chapter 8 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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