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2D motion of a projectile

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A block of mass m slides down a frictionless incline. The block is released at height h above the bottom of the loop (see file for drawing of path).

a. What is the force on the inclined track on the block at point A
b. What is the force on the inclined track at point B
c. At what speed does the block leave the track at point B
d. How far from point A does the block land on level ground.
e. Sketch the potential energy of the block. Show total energy on the sketch.

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Solution Summary

The 7 page-long solution demonstrates in a step by step manner how to apply energy conservation to describe the motion of a mass in two dimensions.

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Please see the attachment.

Square roots all over the place.

I left numbers out of this.

At every point along the track, the total mechanical energy is conserved.
We measure all heights with respect to point A.

The initial energy is all potential:

At point A the energy is purely kinetic (the height at this point is zero)

Conservation of energy requires:

Thus:

There are two forces acting on the block at point A.

One is the normal force that the track is applying on the block due to gravity (the block applies its weight to the track, so the track pushes back with equal magnitude and opposite ...

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