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Gravitational force - the x and/or the z-direction In the...

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Gravitational force A ball moving upwards in the gravitational field of the earth will lose its kinetic energy and come momentarily to rest at its highest point. The ball than reverses its direction, steadily regaining its kinetic energy that was lost on the way up. When the ball arrives at its starting point it will have a kinetic energy equal to its initial kinetic energy. The work done by the gravitational force on the ball is negative during the upwards motion while it is positive on the way down. The work done when the ball returns to its original position is zero. The potential energy due to the gravitational force can be calculated where the potential energy at y = 0 is defined to be zero. Conservation of energy for the earth- ball system now shows This equation holds also for a ball moving in two or three dimensions. Since F g is perpendicular to the horizontal direction, the work done by this force on the ball is zero for a displacement in
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Unformatted text preview: the x and/or the z-direction. In the calculation of the change in the gravitational potential energy of an object, only the displacement in the vertical direction needs to be considered. Sample Problem 8-3 A child with mass m is released from rest at the top of a curved water slide, a height h above the level of a pool. What is the velocity of the child when she is projected into the pool ? Assume that the slide is frictionless. The initial energy consist only out of potential energy (since child is at rest the kinetic energy is zero) E i = m g h where we have taken the potential energy at pool level to be zero. At the bottom of the slide, the potential energy is zero, and the final energy consist only out of kinetic energy Conservation of energy requires that E i = E f Thus or...
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