(a)
Final velocities of both mass after collision.
(a)
Answer to Problem 39P
Both objects after a head-on collision will stick together and move with the same velocity that is
Explanation of Solution
Given:
Object mass is 15 kg. It moves in +x direction at 5.5 m/s. it collides with a mass of 10 kg that is travelling in -x direction at 4 m/s.
After the collision, objects stick together that is they move with equal velocity as a single unit
Formula Used:
According to the conservation of momentum,
Calculation:
Substituting the values in the formula for the conservation of momentum,
Conclusion:
Thus, both objects after a head-on collision will stick together and move with the same velocity that is
(b)
Final velocities of both mass after collision.
(b)
Answer to Problem 39P
After the collision, object with mass
Explanation of Solution
Given:
Object mass is 15 kg. It moves in +x direction at 5.5 m/s. it collides with a mass of 10 kg that is travelling in -x direction at 4 m/s.
The collision is elastic which means,
Formula Used:
According to the conservation of momentum,
Calculation:
After inserting the values in the formula for the conservation of momentum,
Conclusion:
Thus, after the collision, object with mass
(c)
Final velocities of both mass after collision.
To identify: Whether the result obtained is reasonable.
(c)
Answer to Problem 39P
Both objects after a head-on collision, 15 kg object is at rest that is
Yes, it is reasonable.
Explanation of Solution
Given:
Object mass is 15 kg. It moves in +x direction at 5.5 m/s. it collides with a mass of 10 kg that is travelling in -x direction at 4 m/s.
After the collision, 15 kg object is at rest.
Formula Used:
According to the conservation of momentum,
According to the conservation of kinetic energy,
Calculation:
After inserting the values in the formula for the conservation of momentum, we get
Now, calculating change in kinetic energy,
Here, system has lost kinetic energy.
Now, after checking the direction of the system after collision,
Conclusion:
Both objects after a head-on collision, 15 kg object is at rest that is 0 m/s and 10 kg object will move in +x direction with
The result is reasonable.
(d)
Final velocities of both mass after collision.
To identify: Whether the result obtained is reasonable.
(d)
Answer to Problem 39P
Both objects after a head-on collision, 10 kg object is at rest that is
Explanation of Solution
Given:
Object mass is 15 kg. It moves in +x direction at 5.5 m/s. it collides with a mass of 10 kg that is travelling in -x direction at 4 m/s.
After the collision, 10 kg object is at rest that is
Formula Used:
According to the conservation of momentum,
Calculation:
After inserting the values in the formula for the conservation of momentum,
Now, after checking the direction of the system, after collision, 15 kg object will move in +x direction and 10 kg object will be stopped. But, 15 kg object cannot pass the other object moving in the +x direction. If 10 kg object stops, then 15 kg object must move in −x direction. Hence, this result is not reasonable.
Conclusion:
Both objects after a head-on collision, 10 kg object is at rest that is
(e)
Final velocities of both mass after collision.
To identify: Whether the result obtained is reasonable.
(e)
Answer to Problem 39P
Both objects after a head-on collision, 10 kg object is moving in +x direction with velocity
Explanation of Solution
Given:
Object mass is 15 kg. It moves in +x direction at 5.5 m/s. it collides with a mass of 10 kg that is travelling in -x direction at 4 m/s.
After the collision, 15 kg object is moving in negative direction with velocity
Formula Used:
According to the conservation of momentum,
Calculation:
After substituting the values in the formula for the conservation of momentum,
Now, after checking the direction of the system, directions of the system is accurate. But, considering the case of perfectly elastic collision, velocity of both objects is larger in this case. This suggests that both particles have gained kinetic energy which is not possible without any external source or greater initial velocities. Hence, result is not reasonable.
Conclusion:
Both objects after a head-on collision, 10 kg object is moving in +x direction with velocity
Chapter 7 Solutions
Physics: Principles with Applications
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