A440g beanbag slides up a cornhole board (if you’ve never played cornhole before, the board is basically a ramp). the board is tilted 10◦ from the horizontal. the beanbag initially is moving with a speed of 1.21 m/s directly up the ramp. it stops at a certain point, and then slides back down. the coefficients of friction between the board and the beanbag are μ s = . 16 and μ k = . 090.

1. how does the magnitude of the acceleration of the bean bag on the way up compare to the acceleration of the beanbag on the way down? explain your reasoning.

2. how far up the ramp from its initial position does it stop? (cannot assume acceleration = 0)

3. what is the bean bag’s speed when it reaches its initial starting point on its way down?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)