Practice Problems #$6$

Physics $121$

Autumn $2024$

The figure below is the potential$-$energy diagram for a $500$ g particle that is released from rest at A$.$ What are the particle's speeds at B$,$ C$,$ and D$?$

It's been a great day of new, frictionless snow. Julie starts at the top of the $60$ slope shown in the figure below. At the bottom, a circular arc carries her through a $90$ turn, and she then launches off a $3\mathrm{.}0-m-$high ramp. How far horizontally is her touchdown point from the end of the ramp?

A pendulum is formed from a small ball of mass $m$ on a string of length $L.$ As shown in the figure below, a peg is height $h=\frac{L}{3}$ above the pendulum's lowest point. From what minimum angle $$ must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?

In a physics lab experiment, a compressed spring launches a $20$ g metal ball at a $30$ angle. Compressing the spring $20$ cm causes the ball to hit the floor $1\mathrm{.}5$ m below the point at which it leaves the spring after traveling $5\mathrm{.}0$ m horizontally. What is the spring constant?