The box is lifted from the floor with an acceleration of 1 m / s ^ 2. Determine the mass of the box

The box is lifted from the floor with an acceleration of 1 m / s ^ 2. Determine the mass of the box if the tension force of the rope with which the box is lifted is 220N.

a = 1 m / s2.

N = 220 N.

g = 10 m / s2.

m -?

When lifting up, 2 forces act on the box: the force of gravity Ft directed vertically downward, the force N of the rope tension directed vertically upward.

m * a = m * g + N – 2 Newton’s law in vector form.

For projections onto the vertical axis 2, Newton’s law will take the form: m * a = – Fт + N.

N = m * a + Fт.

The force of gravity Ft is determined by the formula: Ft = m * g.

N = m * a + m * g.

N = m * (a + g).

The box mass m will be determined by the formula: m = N / (a + g).

m = 220 N / (1 m / s2 + 10 m / s2) = 20 kg.

Answer: the box has a mass of m = 20 kg.