Question

Верёвка выдерживает груз массой m1=150 кг при вертикальном подъеме его с некоторым ускорением и груз массой m2=750 кг при опускании его с таким же по модулю ускорением. Груз какой массы можно поднимать с помощью этой веревки равномерно?

Answer 1

F=m1*g+m1*a
F=m2*g-m2*a
F=m*g
m1*g+m1*a=m2*g-m2*a
a=g*(m2-m1)/(m1+m2)=9,8*(750-150)/(750+150)=6,53 м/с2
m=F/g=m1*(g+a)/g=150*(9,8+6,53)/9,8=250 кг

Answer 2

Calculation of the Maximum Mass that can be Lifted with the Rope

To determine the maximum mass that can be lifted with the rope, we need to consider the forces acting on the rope during vertical motion.

Let's assume that the acceleration during both lifting and lowering is the same and denoted as 'a'.

When lifting the mass m1 = 150 kg, the tension in the rope will be equal to the weight of the mass plus the force required to accelerate it upwards. The equation for this situation is:

T1 = m1 * g + m1 * a, where g is the acceleration due to gravity.

When lowering the mass m2 = 750 kg, the tension in the rope will be equal to the weight of the mass minus the force required to decelerate it downwards. The equation for this situation is:

T2 = m2 * g - m2 * a.

Since the acceleration is the same in both cases, we can set T1 equal to T2 and solve for the maximum mass that can be lifted:

m_max = (T1 - m1 * g) / a.

Let's substitute the given values into the equation to find the maximum mass that can be lifted with the rope:

m_max = ((m1 * g + m1 * a) - m1 * g) / a = m1.

Therefore, the maximum mass that can be lifted with the rope is 150 kg.

Please note that this calculation assumes ideal conditions and does not take into account factors such as the strength and durability of the rope.