Question

Брусок движется по горизонтальной плоскости прямолинейно с постоянным ускорением 1 м/c2 под действием силы F,направленной вниз под углом 30° к горизонту (см. рисунок). Какова масса бруска, если коэффициент трения бруска о плоскость равен 0,2, а F = 2,7 Н? Ответ округлите до десятых

Answer 1

M*a=F*cosa-u*N (1)
N=m*g-F*sina (2)
Подставим 2 в 1
m*a=F*cosa-u*(m*g-F*sina)
m=F*(cosa+u*sina)/(a+k*g)=2,7*(0,866+0,2*0,5)/(1+0,2*10)=0,87 кг

Answer 2

Calculation of the Mass of the Block

To calculate the mass of the block, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force acting on the block is the component of the force F that is directed downward at an angle of 30° to the horizontal plane.

Let's denote the mass of the block as m and the acceleration as a. The force acting on the block can be calculated using the equation:

F = m * a

Given that the force F is 2.7 N and the acceleration a is 1 m/s², we can substitute these values into the equation to solve for the mass m:

2.7 N = m * 1 m/s²

Simplifying the equation, we find:

m = 2.7 kg

Therefore, the mass of the block is approximately 2.7 kg.

Rounding the Answer

The question asks us to round the answer to the nearest tenth. Since the mass of the block is given in kilograms, which is already rounded to the nearest tenth, we do not need to make any further rounding calculations. Thus, the mass of the block is approximately 2.7 kg.

Conclusion

The mass of the block moving on a horizontal plane with a constant acceleration of 1 m/s² under the influence of a force of 2.7 N directed downward at an angle of 30° to the horizontal plane is approximately 2.7 kg.