Question

Веревка выдерживает груз массой 110 кг при подъеме его с некоторым ускорением, и груз массой 690 кг при опускании его с таким же по модулю ускорением. Какова максимальная масса груза, который может неподвижно висеть на этой веревке?

Answer 1

1)N - m1*g = m1*a
2)m2*g - N = m2*a

выразим  ускорение из уравнений и приравняем
N/m1-g = g-N/m2
N = 2g/(1/m1+1/m2)

для равномерного движения N = mg,
значит m = 2/(1/m1+1/m2) = 2*110*690/(110+690) = 151 800 / 800 = 189.75 кг

Answer 2

Calculation of Maximum Mass of the Hanging Load

To determine the maximum mass of the load that can hang motionless on the rope, we need to consider the forces acting on the rope during both lifting and lowering.

Let's denote the maximum mass of the load as M.

When lifting the load with some acceleration, the tension in the rope can be calculated using Newton's second law:

T = M * (g + a), where T is the tension, M is the mass of the load, g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the upward acceleration.

According to the given information, the rope can support a load of 110 kg when lifted with some acceleration. Therefore, we can write the equation:

110 * (9.8 + a) = T1 Similarly, when lowering the load with the same magnitude of acceleration, the tension in the rope can be calculated as:

T = M * (g - a)

According to the given information, the rope can support a load of 690 kg when lowered with the same acceleration. Therefore, we can write the equation:

690 * (9.8 - a) = T2 To find the maximum mass of the load that can hang motionless on the rope, we need to find the value of M for which T1 = T2.

By equating the two tension equations, we can solve for a:

110 * (9.8 + a) = 690 * (9.8 - a)

Simplifying the equation:

1078 + 110a = 6762 - 690a

Combining like terms:

800a = 5684

Solving for a:

a = 7.105 m/s^2

Now, we can substitute the value of a into one of the tension equations to find the maximum mass M:

110 * (9.8 + 7.105) = M * 9.8

Simplifying the equation:

M = (110 * 16.905) / 9.8

Calculating the value:

M ≈ 188.5 kg

Therefore, the maximum mass of the load that can hang motionless on the rope is approximately 188.5 kg.

Please note that the above calculation assumes ideal conditions and does not take into account factors such as the strength and elasticity of the rope. It is always important to consider safety factors and consult relevant guidelines when dealing with load-bearing applications.

Conclusion

The maximum mass of the load that can hang motionless on the rope is approximately 188.5 kg.