Question

Пасажир, маса якого 60кг,спить на верхній полиці у вагоні потягу, щр рухається зі швидкістю 72 км/год. Визначити мінімальний час гальмування потягу до зупинки, безпечний для пасажира. Коефіцієнт тертя між пасажиром і поверхнею полиці 0,1​

Answer 1

Ответ:

m-60кг

v-72км/год

Fт-0,1H

g-10

______________

t-?

72•60•0.1÷10=43

Answer 2

Problem Analysis

To determine the minimum safe braking time for the train, we need to consider the deceleration required to ensure the passenger's safety. The passenger's mass is 60 kg, and the train's speed is 72 km/h. We also have the coefficient of friction between the passenger and the surface of the berth, which is 0.1.

Calculation of Minimum Safe Braking Time

To calculate the minimum safe braking time, we can use the following steps:

1. Calculate the gravitational force acting on the passenger: \[ F_{\text{gravity}} = m \times g \] where \( m = 60 \, \text{kg} \) (mass of the passenger) and \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity).

\[ F_{\text{gravity}} = 60 \, \text{kg} \times 9.81 \, \text{m/s}^2 \]

This will give us the force due to gravity acting on the passenger.

2. Calculate the maximum frictional force that can be exerted on the passenger: \[ F_{\text{friction}} = \mu \times F_{\text{normal}} \] where \( \mu = 0.1 \) (coefficient of friction) and \( F_{\text{normal}} = F_{\text{gravity}} \) (normal force).

\[ F_{\text{friction}} = 0.1 \times F_{\text{gravity}} \]

This will give us the maximum frictional force that can be exerted on the passenger.

3. Calculate the deceleration required to stop the passenger: \[ a = \frac{F_{\text{friction}}}{m} \] where \( F_{\text{friction}} \) is the maximum frictional force and \( m \) is the mass of the passenger.

\[ a = \frac{F_{\text{friction}}}{m} \]

This will give us the deceleration required to stop the passenger.

4. Calculate the minimum safe braking time: \[ t = \frac{v}{a} \] where \( v = 72 \, \text{km/h} \) (initial speed of the train) and \( a \) is the deceleration required to stop the passenger.

\[ t = \frac{72 \, \text{km/h}}{a} \]

This will give us the minimum safe braking time for the train.

Calculation

Let's perform the calculations based on the given data and the steps outlined above.