Question

Тело массой 3кг соскальзывает с высоты 2м по наклонной плоскости, расположенной под углом а=30° к горизонту. Коэффициент трения м=0,1. Определить работу силы трения при движении тела по наклонной плоскости.

Answer 1

Тело массой m=3кг соскальзывает с высоты h=2м по наклонной плоскости, расположенной под углом а=30° к горизонту. Коэффициент трения k=0,1. Определить работу силы трения при движении тела по наклонной плоскости.

А = -Fтр*L
sina=h/L
L=h/sina
А=-Fтр*h/sina
Fтр=k*N  N= m*g*cosa
Fтр=k*m*g*соsa 
Атр=-k*m*g*h*cosa/sina=-0,1*3*10*0,86*2/0,5=-10,32Дж

Answer 2

A=-f трения*S=к.*N*S=к.*mg*sin30*S=3*10*0.1*1/2*S=-1.5S
S=h/sin30=4 м
А=1.5*4=-6

Answer 3

Problem Analysis

We are given the following information: - Mass of the body, m = 3 kg - Height, h = 2 m - Angle of the inclined plane, α = 30° - Coefficient of friction, μ = 0.1

We need to determine the work done by the force of friction as the body moves along the inclined plane.

Solution

To solve this problem, we can follow these steps:

1. Calculate the gravitational potential energy of the body at the initial height. 2. Calculate the final velocity of the body at the bottom of the inclined plane. 3. Calculate the work done by the force of friction.

Let's calculate each step in detail.

Step 1: Calculate the Gravitational Potential Energy

The gravitational potential energy (PE) of an object is given by the formula:

PE = mgh

where m is the mass of the object, g is the acceleration due to gravity, and h is the height.

Using the given values, we can calculate the gravitational potential energy at the initial height:

PE = (3 kg) * (9.8 m/s^2) * (2 m)

Calculating this, we find:

PE = 58.8 J.

Step 2: Calculate the Final Velocity

To calculate the final velocity of the body at the bottom of the inclined plane, we can use the principle of conservation of mechanical energy. The initial potential energy is converted into kinetic energy at the bottom of the inclined plane.

The formula for the final velocity (v) can be derived as follows:

PE = KE

where KE is the kinetic energy of the body.

The kinetic energy (KE) of an object is given by the formula:

KE = (1/2) * m * v^2

where m is the mass of the object and v is the velocity.

Using the given values, we can calculate the final velocity:

PE = KE

mgh = (1/2) * m * v^2

Simplifying the equation, we find:

v = sqrt(2gh)

Substituting the values, we have:

v = sqrt(2 * 9.8 m/s^2 * 2 m)

Calculating this, we find:

v ≈ 6.26 m/s.

Step 3: Calculate the Work Done by the Force of Friction

The work done by the force of friction can be calculated using the formula:

Work = Force * Distance

The force of friction (F) can be calculated using the formula:

F = μ * m * g * cos(α)

where μ is the coefficient of friction, m is the mass of the body, g is the acceleration due to gravity, and α is the angle of the inclined plane.

The distance (d) can be calculated using the formula:

d = h / sin(α)

Using the given values, we can calculate the work done by the force of friction:

F = μ * m * g * cos(α)

d = h / sin(α)

Work = F * d

Substituting the values, we have:

F = (0.1) * (3 kg) * (9.8 m/s^2) * cos(30°)

d = (2 m) / sin(30°)

Work = F * d

Calculating this, we find:

Work ≈ 10.2 J.

Answer

The work done by the force of friction as the body moves along the inclined plane is approximately 10.2 J.

References

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