Question

Тело массой 10кг начинает тянуть по столу, из состояния покоя(v0=0) с помощью нити под углом 30 градусов к поверхности . Определить ускорение тела, если коэффициент трения 0.1 , сила натяжения нити 14Н.

Answer 1

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Answer 2

Problem Analysis

We are given the following information: - Mass of the body, m = 10 kg - Angle of the string with the surface, θ = 30 degrees - Coefficient of friction, μ = 0.1 - Tension in the string, T = 14 N

We need to determine the acceleration of the body.

Solution

To solve this problem, we can break down the forces acting on the body along the horizontal and vertical directions.

# Vertical Forces

The vertical component of the tension force in the string, Tsinθ, will balance the weight of the body, mg. Therefore, we have:

Tsinθ = mg

# Horizontal Forces

The horizontal component of the tension force in the string, Tcosθ, will provide the force required to overcome friction and accelerate the body. The frictional force, f, can be calculated using the coefficient of friction, μ, and the normal force, N.

f = μN

The normal force, N, is equal to the vertical component of the weight of the body, mgcosθ.

N = mgcosθ

Substituting the value of N in the equation for frictional force, we get:

f = μmgcosθ

The net force acting on the body in the horizontal direction is given by:

Fnet = Tcosθ - f

Since the net force is equal to the mass of the body multiplied by its acceleration, we have:

ma = Tcosθ - f

Substituting the value of f, we get:

ma = Tcosθ - μmgcosθ

Simplifying the equation, we get:

a = (Tcosθ - μmgcosθ) / m

Now we can substitute the given values to calculate the acceleration.

# Calculation

Given: - m = 10 kg - θ = 30 degrees - μ = 0.1 - T = 14 N

Using the equation derived above, we can calculate the acceleration:

a = (Tcosθ - μmgcosθ) / m

Substituting the values, we get:

a = (14 * cos(30) - 0.1 * 10 * 9.8 * cos(30)) / 10

Calculating the expression, we find:

a ≈ 1.47 m/s^2

Therefore, the acceleration of the body is approximately 1.47 m/s^2.

Conclusion

The acceleration of the body, when a mass of 10 kg is pulled along a table with a string at an angle of 30 degrees to the surface, with a coefficient of friction of 0.1 and a tension in the string of 14 N, is approximately 1.47 m/s^2.