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# 16. A cart of mass m is released from a height h above the bottom of a loop of radius R such that it just makes the loop: After completing the loop the cart launche...

## Question

###### 16. A cart of mass m is released from a height h above the bottom of a loop of radius R such that it just makes the loop: After completing the loop the cart launches off the right end of the track, which is a distance H above the ground. The track is frictionless Express your answers algebraically below in terms of the given quantities m, R, H, and g, as needed. (a) [6 pts:] Draw the free body diagram (FBD) for the block at the top if it just makes the loop-the-loop: Use the FBD and knowledge of

16. A cart of mass m is released from a height h above the bottom of a loop of radius R such that it just makes the loop: After completing the loop the cart launches off the right end of the track, which is a distance H above the ground. The track is frictionless Express your answers algebraically below in terms of the given quantities m, R, H, and g, as needed. (a) [6 pts:] Draw the free body diagram (FBD) for the block at the top if it just makes the loop-the-loop: Use the FBD and knowledge of circular motion to determine the speed at the top of the loop. Hint: just make the loop means that the normal force instantaneously vanishes at the very top. (b) [6 pts:] Find the minimum height h to just make the loop-the-loop. Show your work (c) [6 pts ] What is the speed of the cart on the right side of the track after completing the full loop; but just prior to launching off of the edge? (d) [7 pts ] Find the distance d where the cart lands, measured relative to the bottom of the ledge as shown (e) Bonus: [5 pts:] Sketch a velocity versus time graph, with a sep- arate labeled curve for the horizontal and vertical velocity compo- H nents for the motion of the cart just after leaving the end of the track to just before hitting the ground.

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