Anail is partially inserted into a block of wood, with a length of 0.0300 m protruding above the top of the block. to hammer the nail in the rest of the way, you drop a 20.0 kg metal cylinder onto it. the cylinder rides on vertical tracks that exert an upward friction force of 16.0 n on the cylinder as it falls. you release the cylinder from rest at a height of 1.50 m above the top of the nail. the cylinder comes to rest on top of the block of wood, with the nail fully inside the block. use the work-energy theorem to find the speed of the cylinder just as it hits the nail.

v = 5.19 m/s

Explanation:

Using the work-energy theorem:

W = Δk

where W is the work and Δk is the change in the kinetic energy

Now the work of all the system is equal to:

where M is the mass, g the gravity, d the distance and the friction force, it means that Mgd is the work of the gravitational force and is the work of the friction force

Also, the kinetic energy could be calulate by:

K =

where M is the mass and V the velocity.

Replacing:

Solving for V, we get:

v = 5.19 m/s

im sorry i dont know

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.