Question

Помогите с решением !! ПОЖАЛУЙСТА. С вершины холма длиной 5м и высотой 3м начинает скользить небольшое тело массой 4 кг. Коэффициент трения между телом и холмом равен 0,2. Определите ускорение,с котором движется тело.

Answer 1

Problem Analysis

To determine the acceleration of the body sliding down the hill, we need to consider the forces acting on the body. The main forces involved are the gravitational force and the frictional force. The gravitational force acts vertically downward, while the frictional force acts parallel to the surface of the hill and opposes the motion of the body.

Solution

To find the acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be expressed as:

ΣF = m * a

In this case, the net force is the difference between the gravitational force and the frictional force:

ΣF = F_gravity - F_friction

The gravitational force can be calculated using the formula:

F_gravity = m * g

where m is the mass of the body and g is the acceleration due to gravity (approximately 9.8 m/s^2).

The frictional force can be calculated using the formula:

F_friction = μ * N

where μ is the coefficient of friction and N is the normal force. The normal force is equal to the component of the gravitational force perpendicular to the surface of the hill, which can be calculated as:

N = m * g * cos(θ)

where θ is the angle of inclination of the hill.

Now, let's calculate the acceleration using the given values.

Given: - Length of the hill (base): 5 m - Height of the hill: 3 m - Mass of the body: 4 kg - Coefficient of friction: 0.2

First, let's calculate the angle of inclination (θ) using trigonometry:

θ = arctan(height/base) = arctan(3/5)

Using a calculator, we find that θ is approximately 30.96 degrees.

Next, let's calculate the gravitational force:

F_gravity = m * g = 4 kg * 9.8 m/s^2

Using a calculator, we find that F_gravity is approximately 39.2 N.

Now, let's calculate the normal force:

N = m * g * cos(θ) = 4 kg * 9.8 m/s^2 * cos(30.96 degrees)

Using a calculator, we find that N is approximately 33.8 N.

Finally, let's calculate the frictional force:

F_friction = μ * N = 0.2 * 33.8 N

Using a calculator, we find that F_friction is approximately 6.76 N.

Now, we can calculate the net force:

ΣF = F_gravity - F_friction = 39.2 N - 6.76 N

Using a calculator, we find that ΣF is approximately 32.44 N.

Finally, we can use Newton's second law to find the acceleration:

ΣF = m * a

Substituting the values, we have:

32.44 N = 4 kg * a

Simplifying the equation, we find:

a = 32.44 N / 4 kg

Using a calculator, we find that the acceleration (a) is approximately 8.11 m/s^2.

Therefore, the body is moving down the hill with an acceleration of approximately 8.11 m/s^2.

Answer

The body is moving down the hill with an acceleration of approximately 8.11 m/s^2.