Concept explainers
(a)
Whether the child-earth system is isolated or not.
(a)

Answer to Problem 13P
Therefore, the child-earth system is isolated as the only force that can do work on the child is her weight.
Explanation of Solution
The mass of the child is
In the child-earth system, the total work on the child is done by the gravitation force (her weight) only as there is no friction and the air resistance is ignored. The work done by the normal force of the slide is zero because her displacement is perpendicular to the normal force.
Hence, the child-earth system is an isolated system.
Conclusion:
Therefore, the child-earth system is isolated as the only force that can do work on the child is her weight.
(b)
Whether there is a non-conservative force acting within the system or not.
(b)

Answer to Problem 13P
Therefore, there is no non conservative force acting within the system because there is no frictional force.
Explanation of Solution
Only the weight of the child does work whereas the normal force does no work since the displacement is always perpendicular to the normal force.
The child-earth system is isolated so, there is no loss of energy. There is no non- conservative force acting within the system because frictional force is absent here.
Conclusion:
Therefore, there is no non conservative force acting within the system because there is no frictional force.
(c)
The total energy of the earth-child system when the child is at the top of the water slide.
(c)

Answer to Problem 13P
The total energy of the earth-child system when the child is at the top of the water slide is
Explanation of Solution
Write the formula to calculate the total energy at the top of the water slide
Here,
Write the formula to calculate the potential energy of the system at the top of the water slide
Here,
As the child starts from rest therefore, the kinetic energy at the top is zero.
Substitute
Conclusion:
Therefore, the total energy of the earth child system when the child is at the top of the water slide is
(d)
The expression for the total energy of the system at the launching point.
(d)

Answer to Problem 13P
The total energy of the system at the launching point is
Explanation of Solution
The mass of the child is
Write the formula to calculate the total energy at the launching point of earth child system
Here,
Write the formula to calculate the potential energy of the system at the launching point of the water slide
Write the formula to calculate the kinetic energy of the system at the launching point of the water slide
Here,
Substitute
Conclusion:
Therefore, the total energy of the earth child system at the launching point is
(e)
The expression for the total energy of the system at the highest point in her projectile motion.
(e)

Answer to Problem 13P
The total energy of the system at the highest point of the projectile motion is
Explanation of Solution
Write the formula to calculate the total energy at the highest point in the projectile motion of earth child system
Here,
Write the formula to calculate the potential energy of the system at the highest point of her projectile motion
Here,
Write the formula to calculate the kinetic energy of the system at the highest point of her projectile motion
Here,
Substitute
Conclusion:
Therefore, the total energy of the system at the highest point of the projectile motion is
(f)
The speed of child at launching point.
(f)

Answer to Problem 13P
The speed of child at launching point is
Explanation of Solution
As the total energy of the system remains conserved at every point therefore,
Substitute
Conclusion:
Therefore, the speed of child at launching point is
(g)
The maximum airborne height
(g)

Answer to Problem 13P
The maximum airborne height
Explanation of Solution
Write the formula to calculate the maximum height
Substitute
The horizontal component of velocity
Substitute
Substitute
Conclusion:
Therefore, the speed of child at launching point is
(h)
Whether the answers would be same if the waterslide were not frictionless.
(h)

Answer to Problem 13P
Therefore, the answers would not be same if the waterslide were not frictionless.
Explanation of Solution
Due to the presence of frictional force, the total mechanical energy of the system would not conserve. There would be some frictional losses. So, the kinetic energy of the child at every point after the top of the slide would be less than the kinetic energy when there is no friction.
Thus, less kinetic energy means, her launch speed, maximum height and final speed would also be less.
Conclusion:
Therefore, the answers would not be same if the waterslide were not frictionless.
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Chapter 8 Solutions
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