Concept explainers
(a)
Time of flight of the medicine from the syringe into the child’s mouth.
(a)
Answer to Problem 76PQ
Time of flight of the medicine from the syringe into the child’s mouth is
Explanation of Solution
Write the equation to find the distance travelled by medicine into the mouth of child.
Here,
The syringe is fixed horizontally, so the initial components of velocities are zero. That is
Put
Conclusion:
Substitute
Therefore, time of flight of the medicine from the syringe into the child’s mouth is
(b)
Speed of medicine while leaving the syringe to the mouth of the child.
(b)
Answer to Problem 76PQ
The speed of the medicine while leaving he syringe to the mouth of the child is
Explanation of Solution
Write the equation to find the horizontal displacement of medicine.
Here,
Rewrite equation (III) to get
Conclusion:
Substitute
Therefore, speed of the medicine while leaving he syringe to the mouth of the child is
(c)
Speed with which mother should push the plunger of the syringe.
(c)
Answer to Problem 76PQ
The speed with which mother should push the plunger of syringe is
Explanation of Solution
Here the medicine pushed by a plunger from a barrel to opening of the syringe. Therefore apply continuity equation to connect the area and velocity of both the region.
Write the continuity equation to the barrel of medicine and the opening of the syringe.
Here,
Replace
Area of the opening of syringe is not given, but the radius is provided.
Write the equation to find the area of the opening of the syringe.
Here,
Rewrite equation (VI) to get
Conclusion:
Substitute
Substitute
Therefore, the speed with which mother should push the plunger of syringe is
(d)
Pressure of medicine in the opening of the syringe.
(d)
Answer to Problem 76PQ
Pressure of medicine at the opening of the syringe is
Explanation of Solution
The pressure experienced by the medicine at the opening of syringe is nothing but the atmospheric pressure. The magnitude of atmospheric pressure is
Conclusion:
Therefore, pressure of medicine at the opening of the syringe is
(d)
Pressure in the barrel of medicine.
(d)
Answer to Problem 76PQ
Pressure of medicine at the barrel is
Explanation of Solution
Here the flow of medicine through is assumed to be an ideal one. Hence we can apply Bernoulli’s law. Bernoulli’s law states that the total mechanical energy stored in the system is a constant.
Write the Bernoulli’s equation.
Here,
Since the medicine is flowing through a horizontal syringe,
Rewrite equation (IX).
Rearrange equation (X) to get
Conclusion:
Substitute
Therefore, pressure of medicine at the opening of the syringe is
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Chapter 15 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
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