A uniform beam of mass m = 2.5 kg and length L = 1.5 m can rotate about an axle

Question

A uniform beam of mass m = 2.5 kg and length L = 1.5 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 5.5 N, F2 = 3 N, F3 = 12.5 N and F4 = 17.5 N. F2 acts a distance d = 0.2 m from the center of mass.

a) Calculate the magnitude ?1 of the torque due to force F1 in N ? m.

b)Calculate the magnitude ?2 of the torque due to force F2 in N ? m.

c) Calculate the magnitude ?3 of the torque due to force F3 in N ? m.

d) Calculate the magnitude ?4 of the torque due to force F4 in N ? m.

e) Calculate the angular acceleration ? of the beam about its center of mass in radians/s2. Let the counter-clockwise direction be positive.

A uniform beam of mass m = 2.5 kg and length L = 1.5 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 5.5 N, F2 = 3 N, F3 = 12.5 N and F4 = 17.5 N. F2 acts a distance d = 0.2 m from the center of mass.

Explanation / Answer

i. torque due to F1=-5.5N*1.5/2=-4.125Nm(assuming the clockwise as negative)

ii)torque due to F2=3*sin45*0.2=0.4243Nm

iii)torque due to F3=12.5*sin 60*0=0

iv)torque T4 due to F4=0

v) angualr accleration=m*r^2(moment of inertia)*angular acc=net torque

=-4.125+0.4243=2.5*0.75^2*alpha

so angualr acc=-2.63rad/s^2

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