With the help of a rope, the load begins to be lifted vertically upwards with uniform acceleration. The rope acts on the load with a force of 63.3N. In 3 seconds, the load was lifted to a height of 12m. What is the weight of the cargo?
N = 63.3 N.
t = 3 s.
h = 12 m.
g = 9.8 m / s2.
V0 = 0 m / s.
When the load is lifted up, 2 forces act on it: gravity Ft directed vertically downward, and rope tension force N directed vertically upward.
m * a = F + N – 2 Newton’s law in vector form.
We will direct the coordinate axis of the OU vertically upward.
For projections on the OU 2 axis, Newton’s law will take the form: m * a = – Ft + N.
N = m * a + Fт.
The force of gravity Ft is determined by the formula: Ft = m * g.
N = m * a + m * g = m * (a + g).
m = N / (a + g).
Since the load begins to move from a state of rest V0 = 0 m / s, then h = a * t ^ 2/2.
a = 2 * h / t ^ 2.
a = 2 * 12 m / (3 s) ^ 2 = 2.7 m / s2.
m = 63.3 N / (2.7 m / s2 + 9.8 m / s2) = 5 kg.
Answer: the mass of the cargo is m = 5 kg.
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