# The mass of a 5-liter helium-filled baby balloon is 5 g. What is the maximum weight you can hang from

**The mass of a 5-liter helium-filled baby balloon is 5 g. What is the maximum weight you can hang from this balloon so that it hangs in the air? The weight of the thread on which the weight is suspended is 0.45 g. Air density = 1.29 kg / m3; density of helium = 0.18 kg / m3 cubic**

m = 30 kg.

g = 10 m / s2.

a = 0 m / s2.

∠α = 30 °.

μ = 0.5.

Fт -?

Let us write Newton’s 2 law in vector form for pulling out a box along an inclined plane: m * a = Ft + m * g + N + Ftr, where Ft is the force with which the body is pulled up, directed along the inclined plane, m * g is the force of gravity , N is the reaction force of the surface of the inclined plane, Ftr is the friction force.

Since, according to the condition of the problem, it is pulled uniformly a = 0 m / s2, then formula 2 of Newton’s law will take the form: 0 = Ft + m * g + N + Ftr. The action of all forces on the body is compensated.

We write 2 Newton’s law for projections on the coordinate axes:

ОХ: 0 = Ft – Ftr – m * g * sinα.

OU: 0 = – m * g * cosα + N.

Ft = Ftr + m * g * sinα.

N = m * g * cosα.

The friction force of the box on the inclined plane Ftr is expressed by the formula: Ftr = μ * N = μ * m * g * cosα.

The force Ft with which the box is pulled will be determined by the formula: Ft = μ * m * g * cosα + m * g * sinα = m * g (μ * cosα + sinα).

Ft = 30 kg * 10 m / s2 * (0.3 * 0.866 + 0.5) = 228 N.

Answer: for uniform pulling of the box along an inclined plane, it is necessary to apply a force Fт = 228 N.