## Tuesday, May 1, 2018

### Unizor - Physics - Mechanics - Kinematics - Frame of Reference - Problems 1

Notes to a video lecture on http://www.unizor.com

Kinematics Problems 1

The problems below assume all frames of references related to the ground (where people, trains, cars, rivers etc. participate in motion) to be inertial.

Problem 1

A passenger sitting at the window of a bullet train going with a speed
230 km/hour is watching how another train that has 30 cars 20 meters
each going in the opposite direction with a speed 130 km/hour passes by.

He is looking straight perpendicularly to the track (no picking left or right).

During what time interval T will this passenger be able to see the other train?

T = 6 sec.

Problem 2

The distance between two points along a straight and uniformly flowing
river is 198 km. It takes 11 hours for a ship to go from one point to
another against the river's flow and only 9 hours to go along the flow.

Considering the ship's engine works always in the same regime, what is the speed v of the water flow in the river?

v = 2 km/hour.

Problem 3

A person on his way to work always walked up the escalator from the
underground train station and counted his steps. One day he walked with
certain constant speed and counted 24 steps. Another day he has doubled
his own speed and counted 32 steps on the escalator.

Then on some day the escalator did not work and the person walked all the way up.

How many steps did this person count on his way up on this not working escalator?

48 steps.

Problem 4

Points A and B are located along a straight road.

Car #1 goes from A to B first half a distance with a speed u and another half a distance - with a speed v.

Car #2 spends half a time of its trip from A to B going with a speed u and another half a time - going with a speed v.

What are average speeds s1 and s2 of each car?

s1 = 2uv/(u+v)

(harmonic mean),

s2 = (u+v)/2

(arithmetic mean).

Problem 5

The wheels of a car in uniform motion along a straight line are spinning
making N revolutions per second. The diameter of the wheels is D
meters.

What is the speed v of a car?

v = π·D·N.

Problem 6

A funicular is constructed with two cars sliding on rails up and down a
mountain, connected by a cable passed through a wheel on the top of a
mountain. As a wheel rotates, one car goes up, while another goes down.
Then the wheel rotates in an opposite direction and the car that was at
the bottom of a mountain goes up, while the car on the top goes down.

As cars pass each other with constant speed, their relative to each other speed equals to v.

The diameter of the wheel on the top that drives the cars is D. What is an angular speed ω of this wheel at that moment of cars passing each other?