Work and Energy

Gravity Physics


<div class="wp-block-create-block-problemblock">A spherical non rotating planet has a radius R and a uniform density ##ho## throughout its volume.  Suppose a narrow tunnel were drilled through the planet along one of its diameters as shown in the figure below, in which a small ball of mass m could move freely under the influence of gravity.  Let r be the distance of the ball from the center of the planet.  Suppose the ball is dropped into the tunnel from rest at the planet&#8217;s surface.<br /><img src="/old/images/gravityphysics.gif"  alt="physics gravity problem ><br />A. Show the magnitude of the force of the ball at a distance r < R from the center of the planet is given by F = -Cr, where C = ##\frac{4}{3}\pi G ho m##<br />B. Graph the force F on the ball as a function of distance r from the center of the planet<br />C. Determine the work done by gravity as the ball moves form the surface to the center of the planet<br />D.  Determine the speed of the ball when it reaches the center of the planet.<br />E. Fully describe the subsequent motion of the ball from the time it reaches the center of the planet<br">F.  Write an equation that could be used to calculate the time it takes the ball to move from point P to the center of the planet.</div>


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