Question

Тіло масою 18 кг починає рухатись з стану спокою по похилій площині, розташованій під кутом 45 0 до горизонту, під дією сили тяги 50 Н, яка напрямлена паралельно площині вниз. Який шлях пройде тіло і яку швидкість придбає через 2 с після початку руху, якщо коефіцієнт тертя дорівнює 0,05?​

Answer 1

Ответ:

≈ 19 м

Объяснение:

m = 18 кг

α = 45°

F = 50H

t₁ = 2 c

μ = 0.05

g = 10 H/кг

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s₁ - ?

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По 2-му закону Ньютона

ma = F + mg · sin α - Fтр

Сила трения

Fтр =  mgμ · cos α

Ускорение тела

а = g · (sin α - μ · cos α) + F/m

a = 10 · (0,7071 - 0,05 · 0,7071) + 50/18

а = 9,495 (м/с²)

При равноускоренном движении из состояния покоя пройденное расстояние вычислим по формуле

s₁ = 0.5 at₁² = 0.5 · 9.495 · 2² = 18.99 (м) ≈ 19 м

Answer 2

Problem Analysis

The problem describes a body with a mass of 18 kg starting to move from rest on an inclined plane at a 45-degree angle to the horizon. The body is subjected to a 50 N force of gravity directed parallel to the plane. The coefficient of friction is given as 0.05. We are asked to find the distance traveled by the body and the velocity it attains after 2 seconds.

Calculating Distance Traveled

To calculate the distance traveled by the body, we can use the equation for the displacement on an inclined plane: \[ s = ut + \frac{1}{2}at^2 \] where: - \( s \) = distance traveled - \( u \) = initial velocity (0 m/s as the body starts from rest) - \( a \) = acceleration - \( t \) = time

The acceleration can be calculated using the force of gravity and the coefficient of friction: \[ a = g \sin(\theta) - \mu g \cos(\theta) \] where: - \( g \) = acceleration due to gravity (9.81 m/s^2) - \( \theta \) = angle of the incline (45 degrees) - \( \mu \) = coefficient of friction

Let's calculate the distance traveled using the given values.

Calculating Velocity

To calculate the velocity attained by the body after 2 seconds, we can use the equation: \[ v = u + at \] where: - \( v \) = final velocity - \( u \) = initial velocity (0 m/s as the body starts from rest) - \( a \) = acceleration - \( t \) = time

We already have the acceleration from the previous calculation. Let's calculate the velocity attained after 2 seconds.

Calculation

Using the given values: - Mass (m) = 18 kg - Force of gravity (F) = 50 N - Angle of incline (\( \theta \)) = 45 degrees - Coefficient of friction (\( \mu \)) = 0.05 - Time (t) = 2 seconds

Distance Traveled

The distance traveled by the body can be calculated using the equation: \[ s = ut + \frac{1}{2}at^2 \]

Substituting the values: \[ a = g \sin(\theta) - \mu g \cos(\theta) \] \[ a = 9.81 \times \sin(45) - 0.05 \times 9.81 \times \cos(45) \] \[ a \approx 4.905 - 0.3465 \] \[ a \approx 4.5585 \, m/s^2 \]

\[ s = 0 \times 2 + \frac{1}{2} \times 4.5585 \times 2^2 \] \[ s = 0 + \frac{1}{2} \times 4.5585 \times 4 \] \[ s \approx 9.117 \, m \]

The body will travel approximately 9.117 meters.

Velocity Attained

The velocity attained by the body after 2 seconds can be calculated using the equation: \[ v = u + at \]

Substituting the values: \[ v = 0 + 4.5585 \times 2 \] \[ v \approx 9.117 \, m/s \]

The body will attain a velocity of approximately 9.117 m/s after 2 seconds.