A child of mass m starts from rest and slides without fric- tion from a height h along a slide next to a pool (Fig. P8.13). She is launched from a hcight h/5 into the air over the pool. We wish to find the maxinmum height she reaches above the water in her projectile motion. (a) Is thc child-Earth system isolated or nonisolated? Why? (b) Is there a nonconservative force acting within the system? (c) Define the configuration of the system when the child is at the water level as having zero gravitational potential energy. Express the total energy of the system when the child is at the top of the waterslide.
A child of mass m starts from rest and slides without fric- tion from a height h along a slide next to a pool (Fig. P8.13). She is launched from a hcight h/5 into the air over the pool. We wish to find the maxinmum height she reaches above the water in her projectile motion. (a) Is thc child-Earth system isolated or nonisolated? Why? (b) Is there a nonconservative force acting within the system? (c) Define the configuration of the system when the child is at the water level as having zero gravitational potential energy. Express the total energy of the system when the child is at the top of the waterslide.
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Transcribed Image Text:13. (a) Isolated. The only external influence on the system
is the normal force from the slide, but this force is
always perpendicular to its displacement so it performs
no work on the system. (b) No, the slide is frictionless.
= mgh (d) E = }mgh + şmv
+ gmu
2.
(c) E
system
(e) E
yxtem
8gh
(g) = h(1 - cos' 0) (h) If frietion is
5.
vi-
(F)
(1) v%=
present, mechanical energy of the system would not be con-
served, so the child's kinetic energy at all points after leav-
ing the top of the waterslide would be reduced when com-
pared with the frictionless case. Consequently, her launch
speed and maximum height would be reduced as well,
Transcribed Image Text:A child of mass m starts from rest and slides without fric-
1 tion from a height h along a slide next to a pool (Fig. P8.13).
She is launched from a height h/5 into the air over the pool.
We wish to find the maximum height she reaches above the
water in her projectile motion. (a) Is the child-Earth system
isolated or nonisolated? Why? (b) Is therea nonconservative
force acting within the system? (c) Define the configuration
of the system when the child is at the water level as having
zero gravitational potential energy. Express the total energy
of the system when the child is at the top of the waterslide.
(d) Express the total energy of the system when the child is
at the launching point. (e) Express the total energy of the
system when the child is at the highest point in her
tile motion. (1) From parts (c) and (d), determine her initial
projec-
I.
Figure P8.13
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