Question #125868

A pulley system has the following characteristics;

box one has a mass of 2.0×10 to the power of 3 kg, box 2 is at a 90° angle below box one attached by a rope and has a mass of 4.4×10 to the power of 2 kg, the man on top of box 2 has a mass of 6.0×10 to the power of 1 kg. if all surfaces are frictionless, what is the apparent weight of the man?

box one has a mass of 2.0×10 to the power of 3 kg, box 2 is at a 90° angle below box one attached by a rope and has a mass of 4.4×10 to the power of 2 kg, the man on top of box 2 has a mass of 6.0×10 to the power of 1 kg. if all surfaces are frictionless, what is the apparent weight of the man?

Expert's answer

The problem's solution is based on 2,3 - Newton laws and the connection equation:

"m_1\\vec a_1 = m_1\\vec g+\\vec T_1 + \\vec N_2"

"m_2\\vec a_2 = m_2\\vec g+\\vec N_1 + \\vec P_h" h - human

"m_h\\vec a_h = m_h\\vec g+\\vec T_2"

"\\vec N_2+\\vec N_1 = 0"

"\\vec T_2+\\vec P_h = 0"

"x_1-x_0 + y_0-y_1 = const"

We can take the second derivative from the last eqution and have had: "a_1 = a_2 = a_h = a"

Then in the projection on XY plane, vector equations become next scalar equations:

"m_1a = -N_2" (1)

"m_2a = m_2g+P_h-N_1" (2)

"m_ha_h = m_hg-T_2" (3)

"N_2-N_1=0" (4)

"T_2-P_h=0" (5)

"a_1 = a_2 = a_h = a" (6)

This system of equations we can solve with respect to a:

"a = \\frac{m_1+m_h}{m_2+m_h-m_1}g"

And from (3),(5) get "P_h"

"P_h = \\frac{m_1m_h}{m_2+m_h-m_1}g"

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