A50 kg box sits at rest on a 30 degree ramp where the coef of static friction is 0.5773 what is the normal force on the box

424.3 N

Explanation:

In order to understande the normal force on the box, we have to consider only the forces acting along the direction perpendicular to the surface of the ramp.

In fact, there are only to forces acting along this direction:

- The normal force, N, which pushes upward perpendicular to the ramp

- The component of the weight of the box perpendicular to the ramp, which pushes downward (perpendicular to the ramp), and which is equal to

where m = 50 kg is the mass of the box, g = 9.8 m/s^2 is the acceleration due to gravity, and is the angle of the ramp.

Since the box is in equilibrium in the direction perpendicular to the ramp, these two forces must be equal, so we find:

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

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.