The figure a shows a horizontal uniform beam of mass m_b and length L that is su

Question

The figure a shows a horizontal uniform beam of mass m_b and length L that is supported on the left by a hinge attached to a wall and on the right by a cable at angle theta with the horizontal. A package of mass m s positioned on the beam at a distance x from the left end. The total mass is m_b + m_p = 60.8 kg. The figure b gives the tension T in the cable as a function of the package's position given as a fraction x/L of the beam length. The scale of the Taxis is set by T_a = 500 N and T_b = 700 N. Evaluate (a) angle theta, (b) mass m_b and (c) mass m_p.

Explanation / Answer

under equlibrium consition the net torque is zero

T L sin theta - mp gx - mb g ( L/2) = 0

This can be written in the form of a straight line (in the graph) with

T = ( slop) x/L + y intercept

slope = mp g/ sin theta

y intercept = mbg/ 2 sin theta

sin theta = 60.8 g/ 1200

theta = sin^-1 ( 595.84/1200)= 29.77 dehre

200 = mbg/ sin 29.77

mb = 200 sin 29.77/ 9.8

=10.13 kg

mb = 60.8 kg- 10.13 kg = 50.66 kg

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