Question

Сани массой М = 24 кг находятся на гладком катке. Мальчик массой m = 16 кг, находящийся на санях, держит верёвку, которую тянут с силой F = 10 Н. С каким ускорением будут двигаться сани? Коэффициент трения мальчика о поверхность саней равен 0,4. Трением саней о лед пренебречь.

Answer 1

Может, решил правильно, а может - и нет

Answer 2

Problem Analysis

We are given the following information: - Mass of the sleds (sani), M = 24 kg. - Mass of the boy, m = 16 kg. - Force applied by the boy, F = 10 N. - Coefficient of friction between the boy and the sleds, μ = 0.4. - We need to find the acceleration of the sleds.

To solve this problem, 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. We can also consider the force of friction between the boy and the sleds.

Solution

Let's start by calculating the force of friction between the boy and the sleds. The force of friction can be calculated using the equation:

F_friction = μ * N

Where: - F_friction is the force of friction - μ is the coefficient of friction - N is the normal force

The normal force is equal to the weight of the boy, which can be calculated as:

N = m * g

Where: - m is the mass of the boy - g is the acceleration due to gravity (approximately 9.8 m/s^2)

Substituting the values, we can calculate the force of friction:

F_friction = μ * N = μ * m * g

Next, we can calculate the net force acting on the sleds. The net force is equal to the force applied by the boy minus the force of friction:

Net Force = F - F_friction

Finally, we can use Newton's second law of motion to calculate the acceleration of the sleds:

Net Force = M * a

Where: - M is the mass of the sleds - a is the acceleration of the sleds

We can rearrange the equation to solve for the acceleration:

a = Net Force / M

Let's calculate the acceleration using the given values.

Calculation

Given: - M = 24 kg (mass of the sleds) - m = 16 kg (mass of the boy) - F = 10 N (force applied by the boy) - μ = 0.4 (coefficient of friction)

First, let's calculate the force of friction: F_friction = μ * m * g

Substituting the values: F_friction = 0.4 * 16 kg * 9.8 m/s^2

Now, let's calculate the net force: Net Force = F - F_friction

Substituting the values: Net Force = 10 N - (0.4 * 16 kg * 9.8 m/s^2)

Finally, let's calculate the acceleration: a = Net Force / M

Substituting the values: a = (10 N - (0.4 * 16 kg * 9.8 m/s^2)) / 24 kg

Now, let's calculate the values.

Calculation Results

Using the given values, we can calculate the acceleration of the sleds.

F_friction = 0.4 * 16 kg * 9.8 m/s^2 = 62.72 N

Net Force = 10 N - 62.72 N = -52.72 N

a = (-52.72 N) / 24 kg = -2.1967 m/s^2

Therefore, the sleds will have an acceleration of approximately -2.1967 m/s^2. The negative sign indicates that the sleds will be moving in the opposite direction of the force applied by the boy.

Please let me know if I can help you with anything else.