Many of us had to decide at school or university physics problems, which can be both simple and complex. Solving various physics problems we understand the important role they play in a physics course. Therefore, not a single physics course can do without them. And exactly physics problems are presented on this page in a small number with their solutions.
Physics problems from the section Kinematics
A stone is thrown vertically upward at a speed of 20 m/s. How long will it take for it to fall to Earth? What is the greatest height reached by the stone?
Solution.
The height at which the stone will end up after time t is determined by the formula:
h = V 0 t - 0.5 gt 2 .
When falling to Earth, the altitude is zero. Thus, to determine the time of falling of the stone we obtain the equation
V 0 t - 0.5gt 2 = 0,
(V 0 - 0.5gt)t = 0.
From here, since t ≠ 0, then we get
V0 = 0.5gt = 0
t = 2V 0 /g = 2·20m/s / 9.81 m/s 2= 4.077 s.
To determine the maximum lifting height, note that at the highest point the speed of the stone is zero, that is
V = V 0 - gt = 0.
Hence, t = V 0 / g. Then the greatest height
h max = (V 0) 2 /g - 0.5g(V 0)/g) 2 = 0.5(V 0) 2 /g =
0.5(20 m/s) 2 /9.81 m/s 2 = 81.549 m.
The wheel rotates around its axis, making 20 revolutions per second. The radius of the wheel is 75 centimeters. What is the linear speed of points on the rim of the wheel and points located at a distance equal to half the radius from the center of the wheel?
Solution.
Linear V and angular velocity ω are related by the relation V = ωR. Here R- distance from the point to the axis of rotation.
Angular velocity is ω = 2π n. Let's substitute this expression into the equation for linear speed. We get V= 2πR n. Substituting the data from the problem conditions into the last equality, we obtain the linear speed: for points lying on the wheel rim V = 2π·20 s -1 ·0.75 m = 94.2 m/s; and for points lying in the middle of the radius V = 2π·20 s -1 ·0.375 m = 47.1 m/s .
As we see, the latter physics problems Quite a simple solution.
A car passes a motorcyclist at a speed of 108 kilometers per hour at the same time when the motorcyclist starts to move away and moves with an acceleration of 1 m/s 2 in the direction of the car. After what time will the motorcyclist catch up with the car and at what distance from his starting point? What speed will the motorcyclist have?
Solution.
The movement of a car during uniform motion is determined by the formula S = Vt .
The motorcyclist moves with uniform acceleration and his displacement is determined by the formula
S = at 2 /2.
At the moment when the motorcyclist overtakes the car, their movements will be the same. Hence,
S = at 2 /2 = Vt.
Hence the time during which the motorcyclist will catch up with the car is equal to t = 2V/a. Vehicle speed V= 30 m/s. That's why
t= 2·(30m/s)/(1m/s2) = 60 s = 1 minute.
The distance from the starting point, assuming that the car and motorcycle were moving along a straight section of the road, is equal to the movement of the motorcyclist, as well as the motorist, for the found time, namely
S = Vt= (30 m/s)·(60 s) = 1800 m = 1.8 km.
In this case, the speed of the motorcyclist will reach the value
V = at= 1m/s 2 60 s = 60 m/s = 216 km/h.
Physics problems from section Dynamics
Two plasticine balls, having masses of 10 grams and 16 grams, move in a vacuum with enormous speeds of 200 m/s and 250 m/s towards each other and collide, sticking together. At what speed will the sticky plasticine ball move?
Solution.
Ball impulses before collision
P 1 = m 1 V 1 ; P 2 = m 2 V 2 .
Momentum of a stuck ball after a collision
P = (m 1 + m 2)V.
Here V- the speed of the stuck ball after the collision.
Since the second ball is larger than the first and moves at a higher speed, it is reasonable to make the assumption, without limiting the generality of the solution, that the stuck together single plasticine ball will move in the direction of the initial movement of the second ball.
According to the law of conservation of momentum
P
1 + P
2 = P
.
Here, as usual, vector quantities are indicated in bold.
In projection onto the direction of movement of the second ball, taking into account the direction of the first ball and a fair assumption about the direction of movement of a single stuck together ball, we obtain
m 2 V 2 - m 1 V 1 = (m 1 + m 2)V
From the resulting equation we find the speed of the stuck ball
V = (m 2 V 2 - m 1 V 1)/(m 1 + m 2) =
= (0.016kg·250m/s - 0.01kg·200m/s)/(0.016kg + 0.01kg) = 76.923 m/s.
Presented above and solved physics problems, could be drawn up in part of their solution with drawings, but as we see, drawings are not necessary for their correct solution. The drawings serve to better understand the progress of the solution.
What is the stiffness of a vertical spring if a load weighing 600 kg compresses it by 2 cm?
Solution.
The force of gravity acts on the spring G = mg, which is balanced by the elastic force of the compressed spring F = kx. Based on this, we equate these forces F=G or kx = mg. From here we get
k = mg/k= 600kg·9.81m/s 2 /0.02m = 294300 N/m.
Thermodynamics. Gas laws.
Find the mass of one cubic meter of air at normal atmospheric pressure and the melting temperature of ice. The molar mass of air is 0.029 kg/mol.
Solution.
It is no secret that the melting temperature of ice is T= 273 K or 0 C, and normal atmospheric pressure is p= 10 5 Pa.
According to the Mendeleev-Clapeyron law
pV = mRT/μ.
From this equation we get
m = pVμ/(RT).
Here R= 8.31 J/K mol - universal gas constant.
Substituting numerical data, we get
m= 10 5 Pa · 1 m 3 · 0.029 kg/mol/(8.31 J/K · mol ·273 K) = 1.278 kg.
An ideal gas at a pressure of 80 kPa occupies a volume of 320 liters. At constant temperature, this gas is compressed to a volume of 260 liters. How did the gas pressure change?
Solution.
The process is isothermal. Therefore, we can apply the Boyle-Marriott law, according to which
p 1 V 1 = p 2 V 2,
from which we get
p 2 = p 1 V 1 /V 2= 80 kPa 320 l/260 l = 98.46 kPa.
We looked at some very simple physics problems. On our website you will find solutions from various sections and problem books in physics and mathematics. If you are unable to find a solution to your physics problems using this link, you can simply order it.
When George W. Ferris built the world's first Ferris wheel for the World's Columbian Exposition in Chicago in 1893, he began the process of popularizing such an unusual and interesting attraction. The height of the new product was 75 meters, and two steam engines were responsible for its rotation.
This Ferris wheel was completely dismantled in 1904, but over the years thousands of similar attractions have been installed in different countries of the world.
Ferris wheels come in a variety of sizes and can be found in many places, including theme parks and tourist attractions. Below is top 10 tallest Ferris wheels in the world. The data on where the largest Ferris wheel is located is current for 2018.
The ranking opens with the Japanese Ferris wheel, built in 1997 and installed near the Tempozan Market shopping center in Osaka.
This building is decorated with illumination, which notifies about the weather for the coming days. An orange light means the day will be sunny, green lights mean there are a lot of clouds in the sky, and if the blue light comes on, it means it will rain.
9. Cosmo watch 21 – 112.5 meters
This Ferris wheel, built in 1989 in the Japanese city of Yokohama, has long lost its title as the tallest attraction on Earth, but is still the world's largest clock. The number "21" in the name means "21st century".
The current time is displayed on a huge display located in the center of the wheel. The ride on the attraction takes 15 minutes.
The wheel can carry 480 people in 60 cabins, with each cabin accommodating up to eight passengers. On a clear day, you can see the skyscrapers of Shinjuku, the Boso Peninsula and even Mount Fuji from the wheel.
8. Melbourne Star and 5 other attractions - 120 meters
The spokes of this massive Ferris wheel form a seven-pointed star as a tribute to the Australian flag. A ride on the Star of Melbourne will provide you with 30-minute views of the Docklands and nearby areas of the city such as Port Phillip and the CBD.
There are several other 120 meter tall Ferris wheels:
- “Heavenly Dream Fukuoka” - this “high-rise” opened in 2002 in the city of Fukuoka, Japan.
- The Zhengzhou Ferris Wheel opened in 2003 at an amusement park in Henan Province, China.
- The Changsha Ferris Wheel opened in 2004 in Changsha, China.
- The Tianjin Eye attraction opened in 2008 in Tianjin, China.
- The Suzhou Ferris Wheel opened in 2009 in Suzhou, China.
7. Orlando's Eye - 122 meters
The tallest ride on the East Coast opened in 2015. It provides breathtaking views of the city's theme parks, including nearby SeaWorld Orlando and Universal Orlando.
One revolution of the wheel takes 23 minutes. Before boarding the booth, visitors will be shown a mini-film about the construction of the wheel. And when leaving the wheel, riders are offered a free can of Coca-Cola.
6. Red horse – 123 meters
Ferris Wheel - the tallest Ferris wheel in Japan opened in 2016. It rises to a height comparable to the height of a 40-story residential building. For comparison: the highest point is 83 meters (or 28 floors).
All 72 passenger cabins have transparent (and very durable) floors. And in the 18 minutes that the wheel makes a full revolution, its visitors can admire impressive views of the city both from the side windows and from below, if, of course, they dare to look at their feet.
5. London Eye - 135 meters
The top five highest attractions of 2018 opens with one of the most recognizable landmarks in England.
Europe's tallest ride was built in 2000 and was originally called the Millennium Wheel. Each of its 32 capsules can carry 25 passengers, and the entire trip takes about 30 minutes.
More people visit the London Eye every year than the Taj Mahal or the Great Pyramids of Giza.
4. Star of Nanchang – 160 meters
One of the tallest wheels in the world is only 5 meters inferior to its Singaporean competitor. But it opened earlier, in 2006.
Each of the 60 climate-controlled cabins accommodates up to 8 passengers. The attraction is equipped with very beautiful lighting, so in the evening it delights visitors with fantastic illumination.
A ticket to the Nanchang Star will cost only 6 yuan (about 60 rubles). The wheel works around the clock.
3. “Soaring Singapore” – 165 meters
The huge Ferris Wheel, opened in 2008 on the shores of Singapore Bay, provides stunning views of nearby Malaysia and Indonesia. Each of the 28 capsules is the size of a mini-bus and can accommodate 28 passengers. One rotation of the wheel takes half an hour. And to make the trip more fun, you can order champagne and lunch for two in the cabin.
2. High Roller – 168 meters
The attraction, located in the Linq shopping and entertainment district in the famous Las Vegas, opened in 2014. Each glass cabin, equipped with air conditioning, can accommodate up to 40 passengers. Since this is Vegas, drinks are sold right at the base of the wheel and you can take food into the booth. However, there are no slot machines in the capsules, or at least not yet.
Night tickets for the High Roller are more expensive than day tickets, and this is understandable: after all, at night Las Vegas is flooded with lights and looks much more beautiful.
1. New York Ferris Wheel - 191 meters
The largest Ferris wheel in the world is located on the shores of Staten Island.. It offers incredible views of the Atlantic Ocean, the port of New York and, of course, Manhattan. The construction of the giant cost $230 million (of which $7 million was spent on the lighting kit) and can carry 1,440 passengers in one ride. The duration of the trip will be approximately 38 minutes.
When creating the tallest Ferris wheel, American designers were inspired by the London project, but set themselves the task of catching up and surpassing the British. While the London Wheel is equipped with 32 capsules, each of which can accommodate 25 people, the New York Wheel has 36 capsules, with a capacity of up to 40 passengers each. Well, the height of the American Ferris wheel is much greater. However, as early as 2018, it may cede the title of “the tallest Ferris wheel in the world” to the new king of attractions.