A 4 kg block slides across a rough horizontal surface for 5 s. At time t = 5 s, it reaches a speed of 12 m/s at the bottom of a quarter-circle ramp of radius 4 m, where it slides with negligible friction. The coefficient of kinetic friction between the block
and the rough horizontal surface is Mo = 0.2. The block then slides along the ramp until the
block is launched vertically upward. A graph of the block's vertical speed as a function of
time after the block leaves the ramp is shown in Figure 2.

The magnitude of the change in speed of the block as it travels across the rough horizontal surface for 5s is most nearly:

A 2m/s
B 10 m/s
C 12 m/s
D 22 m/s

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

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)

The bar of prob. 5/82 is repeated here. the ends of the 0.4-m bar remain in contact with their re- spective support surfaces. end b has a velocity of 0.5 m/s and an acceleration of 0.3 m/s2 in the di- rections shown. determine the angular accelera- tion of the bar and the acceleration of end a.