   Chapter 5, Problem 46P

Chapter
Section
Textbook Problem

A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine her initial speed V0 at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x. (e) Use the x-component of the answer to part (c) to eliminate from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle θ. (f) Would your answers be the same if the waterslide were not frictionless? Explain. Figure P5.46

(a)

To determine
whether the mechanical energy is conserved in this situation.

Explanation

Yes. The mechanical energy id conserved in this situation. The forces acting on the child when she slides over the frictionless water slide are the gravitational force and the normal force.

The gravitational force is a conservative force. The normal force is a non-conservative force but it is acting perpendicular to the motion of the child. Therefore the work done due to normal force is zero...

(b)

To determine
The gravitational potential energy and the kinetic energy of the child at the top of the waterslide, the launching point and the point where she lands on the pool.

(c)

To determine
The initial speed of the child at the launch point in terms of g and h.

(d)

To determine
The maximum airborne height in terms of h, g and the horizontal speed at the height v0x .

(e)

To determine
The maximum airborne height in terms of h, g and launch angle θ .

(f)

To determine
Whether the answers are same if the waterslide is not frictionless.

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