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Spring Launched Trajectory

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A 2 kg mass is launched from a spring with spring constant $k = 10^4$ N/m compressed a distance $\Delta x$ = 10 cm as shown. It slides up a frictionless ramp to the top and flies off the ramp at a height $h =
1$ m above the ground at an angle of $\theta = 60^\circ$.

Find:

a) The final speed of the mass when it hits the ground.

b) If the ramp is circular with a radius of curvature $R = 2$ m (as drawn on the figure), find the normal force the ramp exerts on the mass just before it flies off the track.

c) If the ramp had friction, would the normal force be greater or smaller at the top? Explain.



Robert G. Brown 2000-12-09