Question

Скорость поезда массой 500 т увеличивается за 1 мин, с 28 км / ч до 40 км / ч найти силу тяги, которую развивает тепловоз если кофициент трения равен 0,8

Answer 1

Ma=F-mgu
u-коофецент трения
a=v/t
t переводим в секунды
v=v1-v2=40-28=12
v переводим в метры в секунду
F=ma+mgu=m(v/t+gu)

Answer 2

Problem Analysis

We are given the following information: - The mass of the train is 500 tons. - The speed of the train increases from 28 km/h to 40 km/h in 1 minute. - The coefficient of friction is 0.8.

We need to find the traction force developed by the locomotive.

Solution

To find the traction force developed by the locomotive, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

In this case, the net force acting on the train is the sum of the traction force and the force of friction. The force of friction can be calculated using the coefficient of friction and the normal force.

Let's break down the solution into steps:

1. Convert the mass of the train from tons to kilograms. 2. Convert the initial and final speeds of the train from km/h to m/s. 3. Calculate the acceleration of the train using the change in speed and time. 4. Calculate the force of friction using the coefficient of friction and the normal force. 5. Calculate the traction force by subtracting the force of friction from the net force.

Let's calculate each step in detail.

Step 1: Convert the mass of the train from tons to kilograms

The mass of the train is given as 500 tons. To convert tons to kilograms, we multiply by 1000 since 1 ton is equal to 1000 kilograms.

Mass of the train in kilograms = 500 tons * 1000 kilograms/ton

Step 2: Convert the initial and final speeds of the train from km/h to m/s

The initial speed of the train is 28 km/h and the final speed is 40 km/h. To convert km/h to m/s, we divide by 3.6 since 1 km/h is equal to 1/3.6 m/s.

Initial speed of the train in m/s = 28 km/h / 3.6 m/s Final speed of the train in m/s = 40 km/h / 3.6 m/s

Step 3: Calculate the acceleration of the train using the change in speed and time

The acceleration of the train can be calculated using the formula:

Acceleration = (Final speed - Initial speed) / Time

In this case, the time is given as 1 minute. To convert minutes to seconds, we multiply by 60 since 1 minute is equal to 60 seconds.

Acceleration = (Final speed of the train in m/s - Initial speed of the train in m/s) / (1 minute * 60 seconds/minute)

Step 4: Calculate the force of friction using the coefficient of friction and the normal force

The force of friction can be calculated using the formula:

Force of friction = Coefficient of friction * Normal force

The normal force is equal to the weight of the train, which can be calculated using the formula:

Weight = Mass * Gravity

In this case, the acceleration due to gravity is approximately 9.8 m/s^2.

Normal force = Mass of the train in kilograms * Acceleration due to gravity

Force of friction = Coefficient of friction * Normal force

Step 5: Calculate the traction force by subtracting the force of friction from the net force

The net force acting on the train is equal to the product of the mass of the train and the acceleration.

Net force = Mass of the train in kilograms * Acceleration

The traction force can be calculated by subtracting the force of friction from the net force.

Traction force = Net force - Force of friction

Let's calculate the values.

Calculation

Step 1: Convert the mass of the train from tons to kilograms: Mass of the train in kilograms = 500 tons * 1000 kilograms/ton

Step 2: Convert the initial and final speeds of the train from km/h to m/s: Initial speed of the train in m/s = 28 km/h / 3.6 m/s Final speed of the train in m/s = 40 km/h / 3.6 m/s

Step 3: Calculate the acceleration of the train using the change in speed and time: Acceleration = (Final speed of the train in m/s - Initial speed of the train in m/s) / (1 minute * 60 seconds/minute)

Step 4: Calculate the force of friction using the coefficient of friction and the normal force: Normal force = Mass of the train in kilograms * Acceleration due to gravity Force of friction = Coefficient of friction * Normal force

Step 5: Calculate the traction force by subtracting the force of friction from the net force: Net force = Mass of the train in kilograms * Acceleration Traction force = Net force - Force of friction

Let's calculate the values.

Calculation

Step 1: Convert the mass of the train from tons to kilograms: Mass of the train in kilograms = 500 tons * 1000 kilograms/ton = 500,000 kilograms

Step 2: Convert the initial and final speeds of the train from km/h to m/s: Initial speed of the train in m/s = 28 km/h / 3.6 m/s ≈ 7.78 m/s Final speed of the train in m/s = 40 km/h / 3.6 m/s ≈ 11.11 m/s

Step 3: Calculate the acceleration of the train using the change in speed and time: Acceleration = (Final speed of the train in m/s - Initial speed of the train in m/s) / (1 minute * 60 seconds/minute) ≈ (11.11 m/s - 7.78 m/s) / (1 minute * 60 seconds/minute) ≈ 0.0556 m/s^2

Step 4: Calculate the force of friction using the coefficient of friction and the normal force: Normal force = Mass of the train in kilograms * Acceleration due to gravity ≈ 500,000 kilograms * 9.8 m/s^2 ≈ 4,900,000 N Force of friction = Coefficient of friction * Normal force ≈ 0.8 * 4,900,000 N ≈ 3,920,000 N

Step 5: Calculate the traction force by subtracting the force of friction from the net force: Net force = Mass of the train in kilograms * Acceleration ≈ 500,000 kilograms * 0.0556 m/s^2 ≈ 27,800 N Traction force = Net force - Force of friction ≈ 27,800 N - 3,920,000 N ≈ -3,892,200 N

Answer

The traction force developed by the locomotive is approximately -3,892,200 N. The negative sign indicates that the force is acting in the opposite direction of motion, which means it is a resisting force.

Please note that the negative value of the traction force indicates that the locomotive is not able to provide enough force to overcome the force of friction and accelerate the train.