Question

Для равномерного подъёма груза массой 100кг по наклонной плоскости прикладывают силу 200Н.Во сколько раз длина наклонной плоскости больше её высоты, если КПД наклонной плоскости равен 80%? Чему равна сила трения при движении груза?

Answer 1

Отношение длины к высоте L/h = 1/sinα
КПД наклонной плоскости равно отношению полезной работы A1=m*g*h к затраченной работе A2 = L*F

A1 / A2 = 0,8
(m*g*h) / (L*F) = 0,8
(150 * 9,8) * sinα / 200 = 0,8
sinα = 0,8 * 200 / (150*9,8) = 0,1088
α=6,246°
L/h = 1/sinα = 1/0,1088 = 9,2

F = Fтр + mg*sinα = 200 Н
Fтр = 200 Н - 100 кг * 9,8 м/с² * 0,1088 = 93,4 Н

Ответ: Длина больше высоты в 9,2 раза, сила трения равна 93,4 Н

Answer 2

Calculation of the Length and Height of the Inclined Plane

To determine the ratio between the length and height of the inclined plane, we can use the concept of mechanical advantage. The mechanical advantage is defined as the ratio of the output force to the input force. In this case, the output force is the force required to lift the load (100 kg) and the input force is the applied force (200 N).

The mechanical advantage (MA) can be calculated using the formula:

MA = output force / input force

Given that the efficiency (η) of the inclined plane is 80% (0.8), we can relate the mechanical advantage to the efficiency using the formula:

MA = 1 / (1 - η)

Substituting the given efficiency value, we can solve for the mechanical advantage:

1 / (1 - 0.8) = 1 / 0.2 = 5

Therefore, the mechanical advantage is 5.

The mechanical advantage is also equal to the ratio of the length of the inclined plane (L) to its height (H):

MA = L / H

Substituting the calculated mechanical advantage, we can solve for the ratio of the length to the height:

5 = L / H

Therefore, the length of the inclined plane is 5 times greater than its height.

Calculation of the Frictional Force

To calculate the frictional force during the movement of the load, we need to consider the forces acting on the load. In this case, the applied force (200 N) is greater than the force required to lift the load (100 kg) against gravity. Therefore, the applied force is sufficient to overcome the force of gravity.

The frictional force (Ff) can be calculated using the formula:

Ff = μ * N

where μ is the coefficient of friction and N is the normal force.

In this case, the normal force is equal to the weight of the load, which can be calculated using the formula:

N = m * g

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

Substituting the given mass value, we can calculate the normal force:

N = 100 kg * 9.8 m/s^2 = 980 N

The coefficient of friction (μ) is not provided in the question. Without this information, we cannot calculate the exact value of the frictional force.

Please provide the coefficient of friction (μ) so that we can calculate the frictional force accurately.